WorldWideScience

Sample records for partial stochastic realization

  1. Stochastic partial differential equations

    CERN Document Server

    Lototsky, Sergey V

    2017-01-01

    Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...

  2. Ambit processes and stochastic partial differential equations

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut

    Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....

  3. On the physical realizability of quantum stochastic walks

    Science.gov (United States)

    Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

    Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

  4. Stochastic partial differential equations an introduction

    CERN Document Server

    Liu, Wei

    2015-01-01

    This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...

  5. Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

    KAUST Repository

    Potsepaev, R.

    2010-09-06

    Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

  6. GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model

    International Nuclear Information System (INIS)

    Takaishi, Tetsuya

    2015-01-01

    The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid Monte Carlo (HMC) algorithm. The HMC algorithm can be parallelized and thus performed on the GPU for speedup. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the HMC algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find that appropriate coding can achieve the similar speedup with CUDA Fortran

  7. Asymptotic problems for stochastic partial differential equations

    Science.gov (United States)

    Salins, Michael

    Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

  8. Effective action for stochastic partial differential equations

    International Nuclear Information System (INIS)

    Hochberg, David; Molina-Paris, Carmen; Perez-Mercader, Juan; Visser, Matt

    1999-01-01

    Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from QFT to the case of

  9. Effective action for stochastic partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Hochberg, David [Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid, (Spain); Centro de Astrobiologia, INTA, Carratera Ajalvir, Km. 4, 28850 Torrejon, Madrid, (Spain); Molina-Paris, Carmen [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Perez-Mercader, Juan [Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid, (Spain); Visser, Matt [Physics Department, Washington University, Saint Louis, Missouri 63130-4899 (United States)

    1999-12-01

    Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from

  10. Stochastic partial differential equations a modeling, white noise functional approach

    CERN Document Server

    Holden, Helge; Ubøe, Jan; Zhang, Tusheng

    1996-01-01

    This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre­ sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in r...

  11. Partial Measurements and the Realization of Quantum-Mechanical Counterfactuals

    Science.gov (United States)

    Paraoanu, G. S.

    2011-07-01

    We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system.

  12. Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps

    OpenAIRE

    Li, Yan; Hu, Junhao

    2013-01-01

    We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.

  13. Numerical methods for stochastic partial differential equations with white noise

    CERN Document Server

    Zhang, Zhongqiang

    2017-01-01

    This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...

  14. Degenerate parabolic stochastic partial differential equations

    Czech Academy of Sciences Publication Activity Database

    span class="emphasis">Hofmanová, Martinaspan>

    2013-01-01

    Roč. 123, č. 12 (2013), s. 4294-4336 ISSN 0304-4149 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : kinetic solutions * degenerate stochastic parabolic equations Subject RIV: BA - General Mathematics Impact factor: 1.046, year: 2013 http://library.utia.cas.cz/separaty/2013/SI/hofmanova-0397241.pdf

  15. Logic for specifying partially observable stochastic domains

    CSIR Research Space (South Africa)

    Rens, G

    2011-07-01

    Full Text Available to place it back on the floor. In situations where the oil-can is full, the robot gets 5 units of reward for grabbing the can, and it gets 10 units for a drink action. Otherwise, the robot gets no rewards. Rewards motivate an agent to behave as desired... with notions of probability. It will be shown how stochastic domains can be specified, including new kinds of axioms dealing with perception and a frame solution for the proposed logic. 1 Introduction and Motivation In the physical real world...

  16. A concise course on stochastic partial differential equations

    CERN Document Server

    Prévôt, Claudia

    2007-01-01

    These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

  17. Bias correction in the realized stochastic volatility model for daily volatility on the Tokyo Stock Exchange

    Science.gov (United States)

    Takaishi, Tetsuya

    2018-06-01

    The realized stochastic volatility model has been introduced to estimate more accurate volatility by using both daily returns and realized volatility. The main advantage of the model is that no special bias-correction factor for the realized volatility is required a priori. Instead, the model introduces a bias-correction parameter responsible for the bias hidden in realized volatility. We empirically investigate the bias-correction parameter for realized volatilities calculated at various sampling frequencies for six stocks on the Tokyo Stock Exchange, and then show that the dynamic behavior of the bias-correction parameter as a function of sampling frequency is qualitatively similar to that of the Hansen-Lunde bias-correction factor although their values are substantially different. Under the stochastic diffusion assumption of the return dynamics, we investigate the accuracy of estimated volatilities by examining the standardized returns. We find that while the moments of the standardized returns from low-frequency realized volatilities are consistent with the expectation from the Gaussian variables, the deviation from the expectation becomes considerably large at high frequencies. This indicates that the realized stochastic volatility model itself cannot completely remove bias at high frequencies.

  18. Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    T. E. Govindan

    2011-01-01

    Full Text Available This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

  19. System Entropy Measurement of Stochastic Partial Differential Systems

    Directory of Open Access Journals (Sweden)

    Bor-Sen Chen

    2016-03-01

    Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

  20. Malliavin Calculus With Applications to Stochastic Partial Differential Equations

    CERN Document Server

    Sanz-Solé, Marta

    2005-01-01

    Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself

  1. Electron thermal confinement in a partially stochastic magnetic structure

    Science.gov (United States)

    Morton, L. A.; Young, W. C.; Hegna, C. C.; Parke, E.; Reusch, J. A.; Den Hartog, D. J.

    2018-04-01

    Using a high-repetition-rate Thomson scattering diagnostic, we observe a peak in electron temperature Te coinciding with the location of a large magnetic island in the Madison Symmetric Torus. Magnetohydrodynamic modeling of this quasi-single helicity plasma indicates that smaller adjacent islands overlap with and destroy the large island flux surfaces. The estimated stochastic electron thermal conductivity ( ≈30 m 2/s ) is consistent with the conductivity inferred from the observed Te gradient and ohmic heating power. Island-shaped Te peaks can result from partially stochastic magnetic islands.

  2. Single realization stochastic FDTD for weak scattering waves in biological random media.

    Science.gov (United States)

    Tan, Tengmeng; Taflove, Allen; Backman, Vadim

    2013-02-01

    This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result.

  3. Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility

    Czech Academy of Sciences Publication Activity Database

    Baruník, Jozef; Kukačka, Jiří

    2015-01-01

    Roč. 15, č. 6 (2015), s. 959-973 ISSN 1469-7688 R&D Projects: GA ČR GA402/09/0965; GA ČR GA13-32263S EU Projects: European Commission 612955 - FINMAP Institutional support: RVO:67985556 Keywords : Stochastic cusp catastrophe model * Realized volatility * Bifurcations * Stock market crash Subject RIV: AH - Economics Impact factor: 0.794, year: 2015 http://library.utia.cas.cz/separaty/2014/E/barunik-0434202.pdf

  4. Improved stochastic approximation methods for discretized parabolic partial differential equations

    Science.gov (United States)

    Guiaş, Flavius

    2016-12-01

    We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

  5. Quantum learning of classical stochastic processes: The completely positive realization problem

    Science.gov (United States)

    Monràs, Alex; Winter, Andreas

    2016-01-01

    Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

  6. Quantum learning of classical stochastic processes: The completely positive realization problem

    Energy Technology Data Exchange (ETDEWEB)

    Monràs, Alex [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Winter, Andreas [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); ICREA—Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys, 23, 08010 Barcelona (Spain)

    2016-01-15

    Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

  7. Quantum learning of classical stochastic processes: The completely positive realization problem

    International Nuclear Information System (INIS)

    Monràs, Alex; Winter, Andreas

    2016-01-01

    Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

  8. Bayesian estimation of realized stochastic volatility model by Hybrid Monte Carlo algorithm

    International Nuclear Information System (INIS)

    Takaishi, Tetsuya

    2014-01-01

    The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model

  9. Variational and potential formulation for stochastic partial differential equations

    International Nuclear Information System (INIS)

    Munoz S, A G; Ojeda, J; Sierra D, P; Soldovieri, T

    2006-01-01

    Recently there has been interest in finding a potential formulation for stochastic partial differential equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangian, and that this potential is able to reproduce all the dynamics of the system once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. (letter to the editor)

  10. Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

    International Nuclear Information System (INIS)

    Ding Chaoliang; Lue Baida; Pan Liuzhan

    2009-01-01

    The unified theory of coherence and polarization proposed by Wolf is extended from stochastic stationary electromagnetic beams to stochastic spatially and spectrally partially coherent electromagnetic pulsed beams. Taking the stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the expressions for the spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic GSMP beams propagating in free space are derived. Some special cases are analyzed. The illustrative examples are given and the results are interpreted physically.

  11. Realization of universal optimal quantum machines by projective operators and stochastic maps

    International Nuclear Information System (INIS)

    Sciarrino, F.; Sias, C.; Ricci, M.; De Martini, F.

    2004-01-01

    Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal antiunitary map. In addition, the contextual realization of the N→M cloning map and of the teleportation of the N→(M-N) universal-NOT (UNOT) gate is analyzed by a very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These include the 1→2 cloning process, the UNOT gate and the quantum tomographic characterization of the optimal partial transpose map of polarization encoded qubits

  12. Stochastic Modeling and Generation of Partially Polarized or Partially Coherent Electromagnetic Waves

    Science.gov (United States)

    Davis, Brynmor; Kim, Edward; Piepmeier, Jeffrey; Hildebrand, Peter H. (Technical Monitor)

    2001-01-01

    Many new Earth remote-sensing instruments are embracing both the advantages and added complexity that result from interferometric or fully polarimetric operation. To increase instrument understanding and functionality a model of the signals these instruments measure is presented. A stochastic model is used as it recognizes the non-deterministic nature of any real-world measurements while also providing a tractable mathematical framework. A stationary, Gaussian-distributed model structure is proposed. Temporal and spectral correlation measures provide a statistical description of the physical properties of coherence and polarization-state. From this relationship the model is mathematically defined. The model is shown to be unique for any set of physical parameters. A method of realizing the model (necessary for applications such as synthetic calibration-signal generation) is given and computer simulation results are presented. The signals are constructed using the output of a multi-input multi-output linear filter system, driven with white noise.

  13. Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

    KAUST Repository

    Potsepaev, R.; Farmer, C.L.

    2010-01-01

    in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

  14. Partial Finite-Time Synchronization of Switched Stochastic Chua's Circuits via Sliding-Mode Control

    Directory of Open Access Journals (Sweden)

    Zhang-Lin Wan

    2011-01-01

    Full Text Available This paper considers the problem of partial finite-time synchronization between switched stochastic Chua's circuits accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, a sliding-mode controller is developed to guarantee the synchronization of switched stochastic master-slave Chua's circuits and for the mean of error states to obtain the partial finite-time stability. Numerical simulations demonstrate the effectiveness of the proposed methods.

  15. Realizations of highly heterogeneous collagen networks via stochastic reconstruction for micromechanical analysis of tumor cell invasion

    Science.gov (United States)

    Nan, Hanqing; Liang, Long; Chen, Guo; Liu, Liyu; Liu, Ruchuan; Jiao, Yang

    2018-03-01

    Three-dimensional (3D) collective cell migration in a collagen-based extracellular matrix (ECM) is among one of the most significant topics in developmental biology, cancer progression, tissue regeneration, and immune response. Recent studies have suggested that collagen-fiber mediated force transmission in cellularized ECM plays an important role in stress homeostasis and regulation of collective cellular behaviors. Motivated by the recent in vitro observation that oriented collagen can significantly enhance the penetration of migrating breast cancer cells into dense Matrigel which mimics the intravasation process in vivo [Han et al. Proc. Natl. Acad. Sci. USA 113, 11208 (2016), 10.1073/pnas.1610347113], we devise a procedure for generating realizations of highly heterogeneous 3D collagen networks with prescribed microstructural statistics via stochastic optimization. Specifically, a collagen network is represented via the graph (node-bond) model and the microstructural statistics considered include the cross-link (node) density, valence distribution, fiber (bond) length distribution, as well as fiber orientation distribution. An optimization problem is formulated in which the objective function is defined as the squared difference between a set of target microstructural statistics and the corresponding statistics for the simulated network. Simulated annealing is employed to solve the optimization problem by evolving an initial network via random perturbations to generate realizations of homogeneous networks with randomly oriented fibers, homogeneous networks with aligned fibers, heterogeneous networks with a continuous variation of fiber orientation along a prescribed direction, as well as a binary system containing a collagen region with aligned fibers and a dense Matrigel region with randomly oriented fibers. The generation and propagation of active forces in the simulated networks due to polarized contraction of an embedded ellipsoidal cell and a small group

  16. Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

    Science.gov (United States)

    Cotter, C J; Gottwald, G A; Holm, D D

    2017-09-01

    In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

  17. Advances in nonlinear partial differential equations and stochastics

    CERN Document Server

    Kawashima, S

    1998-01-01

    In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.

  18. Lp Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

    International Nuclear Information System (INIS)

    Du Kai; Qiu, Jinniao; Tang Shanjian

    2012-01-01

    This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L p -theory is given for the Cauchy problem of BSPDEs, separately for the case of p∈(1,2] and for the case of p∈(2,∞). A comparison theorem is also addressed.

  19. An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Webster, Clayton G [ORNL; Zhang, Guannan [ORNL; Gunzburger, Max D [ORNL

    2012-10-01

    Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.

  20. Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach

    DEFF Research Database (Denmark)

    Bach, Christian; Christensen, Bent Jesper

    process is downward biased. Implied volatility performs better than any of the alternative realized measures when forecasting future integrated volatility. The results are largely similar across the stock market (S&P 500), bond market (30-year U.S. T-bond), and foreign currency exchange market ($/£ )....

  1. Realization of consensus of multi-agent systems with stochastically mixed interactions

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Yongzheng, E-mail: yzsung@gmail.com; Li, Wang [School of Science, China University of Mining and Technology, Xuzhou 221008 (China); Zhao, Donghua [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China)

    2016-07-15

    In this paper, we propose a new consensus model in which the interactions among agents stochastically switch between attraction and repulsion. Such a positive-and-negative mechanism is described by the white-noise-based coupling. Analytic criteria for the consensus and non-consensus in terms of the eigenvalues of the noise intensity matrix are derived, which provide a better understanding of the constructive roles of random interactions. Specifically, we discover a positive role of noise coupling that noise can accelerate the emergence of consensus. We find that the converging speed of the multi-agent network depends on the square of the second smallest eigenvalue of its graph Laplacian. The influence of network topologies on the consensus time is also investigated.

  2. A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

    International Nuclear Information System (INIS)

    Vidal-Codina, F.; Nguyen, N.C.; Giles, M.B.; Peraire, J.

    2015-01-01

    We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method

  3. A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

    KAUST Repository

    Babuška, Ivo; Nobile, Fabio; Tempone, Raul

    2010-01-01

    This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.

  4. Method for measuring the stochastic properties of corona and partial-discharge pulses

    International Nuclear Information System (INIS)

    Van Brunt, R.J.; Kulkarni, S.V.

    1989-01-01

    A new method is described for measuring the stochastic behavior of corona and partial-discharge pulses which utilizes a pulse selection and sorting circuit in conjunction with a computer-controlled multichannel analyzer to directly measure various conditional and unconditional pulse-height and pulse-time-separation distributions. From these measured distributions it is possible to determine the degree of correlation between successive discharge pulses. Examples are given of results obtained from measurements on negative, point-to-plane (Trichel-type) corona pulses in a N 2 /O 2 gas mixture which clearly demonstrate that the phenomenon is inherently stochastic in the sense that development of a discharge pulse is significantly affected by the amplitude of and time separation from the preceding pulse. It is found, for example, that corona discharge pulse amplitude and time separation from an earlier pulse are not independent random variables. Discussions are given about the limitations of the method, sources of error, and data analysis procedures required to determine self-consistency of the various measured distributions

  5. Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data

    KAUST Repository

    Hall, Eric Joseph

    2016-12-08

    We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.

  6. XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

    Science.gov (United States)

    Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

    2013-01-01

    XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method

  7. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

    2016-02-15

    We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

  8. Partial safety factor calibration from stochastic finite element computation of welded joint with random geometries

    International Nuclear Information System (INIS)

    Schoefs, Franck; Chevreuil, Mathilde; Pasqualini, Olivier; Cazuguel, Mikaël

    2016-01-01

    Welded joints are used in various structures and infrastructures like bridges, ships and offshore structures, and are submitted to cyclic stresses. Their fatigue behaviour is an industrial key issue to deal with and still offers original research subjects. One of the available methods relies on the computing of the stress concentration factor. Even if some studies were previously driven to evaluate this factor onto some cases of welded structures, the shape of the weld joint is generally idealized through a deterministic parametric geometry. Previous experimental works however have shown that this shape plays a key role in the lifetime assessment. We propose in this paper a methodology for computing the stress concentration factor in presence of random geometries of welded joints. In view to make the results available by engineers, this method merges stochastic computation and semi-probabilistic analysis by computing partial safety factors with a dedicated method. - Highlights: • Numerical computation of stress concentration factor with random geometry of weld. • Real data are used for probabilistic modelling. • Identification of partial safety factor from SFEM computation in case of random geometries.

  9. Stochastic Partial Differential Equation Solver for Hydroacoustic Modeling: Improvements to Paracousti Sound Propagation Solver

    Science.gov (United States)

    Preston, L. A.

    2017-12-01

    Marine hydrokinetic (MHK) devices offer a clean, renewable alternative energy source for the future. Responsible utilization of MHK devices, however, requires that the effects of acoustic noise produced by these devices on marine life and marine-related human activities be well understood. Paracousti is a 3-D full waveform acoustic modeling suite that can accurately propagate MHK noise signals in the complex bathymetry found in the near-shore to open ocean environment and considers real properties of the seabed, water column, and air-surface interface. However, this is a deterministic simulation that assumes the environment and source are exactly known. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected noise levels within the marine environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. One method is to use Monte Carlo (MC) techniques where simulation results from a large number of deterministic solutions are aggregated to provide statistical properties of the output signal. However, MC methods can be computationally prohibitive since they can require tens of thousands or more simulations to build up an accurate representation of those statistical properties. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a small fraction of the computational cost of MC. We are developing a SPDE solver for the 3-D acoustic wave propagation problem called Paracousti-UQ to help regulators and operators assess the statistical properties of environmental noise produced by MHK devices. In this presentation, we present the SPDE method and compare statistical distributions of simulated acoustic signals in simple models to MC simulations to show the accuracy and efficiency of the SPDE method. Sandia National Laboratories

  10. Transport in Stochastic Media

    International Nuclear Information System (INIS)

    Haran, O.; Shvarts, D.; Thieberger, R.

    1998-01-01

    Classical transport of neutral particles in a binary, scattering, stochastic media is discussed. It is assumed that the cross-sections of the constituent materials and their volume fractions are known. The inner structure of the media is stochastic, but there exist a statistical knowledge about the lump sizes, shapes and arrangement. The transmission through the composite media depends on the specific heterogeneous realization of the media. The current research focuses on the averaged transmission through an ensemble of realizations, frm which an effective cross-section for the media can be derived. The problem of one dimensional transport in stochastic media has been studied extensively [1]. In the one dimensional description of the problem, particles are transported along a line populated with alternating material segments of random lengths. The current work discusses transport in two-dimensional stochastic media. The phenomenon that is unique to the multi-dimensional description of the problem is obstacle bypassing. Obstacle bypassing tends to reduce the opacity of the media, thereby reducing its effective cross-section. The importance of this phenomenon depends on the manner in which the obstacles are arranged in the media. Results of transport simulations in multi-dimensional stochastic media are presented. Effective cross-sections derived from the simulations are compared against those obtained for the one-dimensional problem, and against those obtained from effective multi-dimensional models, which are partially based on a Markovian assumption

  11. Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage.

    Science.gov (United States)

    Johnson, Paul; Howell, Sydney; Duck, Peter

    2017-08-13

    A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD's capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery C , which is a continuous control variable that is changed hourly. Financially, we assume heavy 'system balancing' penalties in continuous time, for deviations of output rate from the commitment C Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

  12. Stochastic Analysis 2010

    CERN Document Server

    Crisan, Dan

    2011-01-01

    "Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa

  13. Intermittency for stochastic partial differential equations driven by strongly inhomogeneous space-time white noises

    Science.gov (United States)

    Xie, Bin

    2018-01-01

    In this paper, the main topic is to investigate the intermittent property of the one-dimensional stochastic heat equation driven by an inhomogeneous Brownian sheet, which is a noise deduced from the study of the catalytic super-Brownian motion. Under some proper conditions on the catalytic measure of the inhomogeneous Brownian sheet, we show that the solution is weakly full intermittent based on the estimates of moments of the solution. In particular, it is proved that the second moment of the solution grows at the exponential rate. The novelty is that the catalytic measure relative to the inhomogeneous noise is not required to be absolutely continuous with respect to the Lebesgue measure on R.

  14. Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

    KAUST Repository

    Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.

    2015-01-01

    We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some

  15. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    International Nuclear Information System (INIS)

    Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.

    2014-01-01

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology

  16. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    Energy Technology Data Exchange (ETDEWEB)

    Das, Sonjoy; Goswami, Kundan [University at Buffalo, NY (United States); Datta, Biswa N. [Northern Illinois University, IL (United States)

    2014-12-10

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.

  17. Stochastic simulations of conditional states of partially observed systems, quantum and classical

    International Nuclear Information System (INIS)

    Gambetta, Jay; Wiseman, H M

    2005-01-01

    In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed, even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix ρ r (t), and if classical, the conditional state will be given by a probability distribution P r (x,t), where r is the result of the measurement. Thus to determine the evolution of this conditional state, under continuous-in-time monitoring, requires a numerically expensive calculation. In this paper we demonstrate a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of N, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems such as arise in modelling realistic (finite bandwidth, noisy) measurement

  18. Fundamentals of stochastic nature sciences

    CERN Document Server

    Klyatskin, Valery I

    2017-01-01

    This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under wh...

  19. Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation

    OpenAIRE

    Bouchard , Bruno; Dang , Ngoc Minh

    2013-01-01

    International audience; We consider a singular with state constraints version of the stochastic target problems studied in Soner and Touzi (2002) and more recently Bouchard, Elie and Touzi (2008), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly suits to market models with proportional transaction costs and to order book liquidation issues. Our main result is a PDE characterization of the associated pri...

  20. Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

    KAUST Repository

    Dolgov, Sergey

    2015-11-03

    We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some quantities of interest (mean, variance, and exceedance probabilities). We assume that the random diffusion coefficient is given as a smooth transformation of a Gaussian random field. In this case, the PCE is delivered by a complicated formula, which lacks an analytic TT representation. To construct its TT approximation numerically, we develop the new block TT cross algorithm, a method that computes the whole TT decomposition from a few evaluations of the PCE formula. The new method is conceptually similar to the adaptive cross approximation in the TT format but is more efficient when several tensors must be stored in the same TT representation, which is the case for the PCE. In addition, we demonstrate how to assemble the stochastic Galerkin matrix and to compute the solution of the elliptic equation and its postprocessing, staying in the TT format. We compare our technique with the traditional sparse polynomial chaos and the Monte Carlo approaches. In the tensor product polynomial chaos, the polynomial degree is bounded for each random variable independently. This provides higher accuracy than the sparse polynomial set or the Monte Carlo method, but the cardinality of the tensor product set grows exponentially with the number of random variables. However, when the PCE coefficients are implicitly approximated in the TT format, the computations with the full tensor product polynomial set become possible. In the numerical experiments, we confirm that the new methodology is competitive in a wide range of parameters, especially where high accuracy and high polynomial degrees are required.

  1. An integrated production-inventory model for the singlevendor two-buyer problem with partial backorder, stochastic demand, and service level constraints

    Science.gov (United States)

    Arfawi Kurdhi, Nughthoh; Adi Diwiryo, Toray; Sutanto

    2016-02-01

    This paper presents an integrated single-vendor two-buyer production-inventory model with stochastic demand and service level constraints. Shortage is permitted in the model, and partial backordered partial lost sale. The lead time demand is assumed follows a normal distribution and the lead time can be reduced by adding crashing cost. The lead time and ordering cost reductions are interdependent with logaritmic function relationship. A service level constraint policy corresponding to each buyer is considered in the model in order to limit the level of inventory shortages. The purpose of this research is to minimize joint total cost inventory model by finding the optimal order quantity, safety stock, lead time, and the number of lots delivered in one production run. The optimal production-inventory policy gained by the Lagrange method is shaped to account for the service level restrictions. Finally, a numerical example and effects of the key parameters are performed to illustrate the results of the proposed model.

  2. Stochastic cooling

    International Nuclear Information System (INIS)

    Bisognano, J.; Leemann, C.

    1982-03-01

    Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron

  3. Stochastic parameterizing manifolds and non-Markovian reduced equations stochastic manifolds for nonlinear SPDEs II

    CERN Document Server

    Chekroun, Mickaël D; Wang, Shouhong

    2015-01-01

    In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

  4. SLIPM - a MAPLE package for numerical solution of Sturm-Liouville partial problems based on a continuous analog of Newton's method. II. Program realization

    International Nuclear Information System (INIS)

    Puzynin, I.V.; Puzynina, T.P.; Tkhak, V.Ch.

    2010-01-01

    SLIPM (Sturm-LIouville Problem in MAPLE) is a program complex written in the language of the computer algebras system MAPLE. It consists of the main program SLIPM.mw and of some procedures. It is intended for a numerical solution with the help of the continuous analog of Newton's method (CANM) of Sturm-Liouville partial problems, i.e. for calculating some eigenvalue of linear second-order differential operator and a corresponding eigenfunction satisfying homogeneous boundary conditions of the general type. SLIPM is the development of the program complexes SLIP1 and SLIPH4 written in the Fortran language. It is added by two new ways of calculating the initial value of iterative parameter τ 0 , by a procedure for calculating a higher precision solution (eigenvalue and corresponding eigenfunction) with the help of Richardson's extrapolation method, by graphical visualization procedures of intermediate and final results of the iterative process and by saving of the results on a disk file. The descriptions of the procedures purposes and their parameters are given

  5. Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

    Science.gov (United States)

    Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

    2016-12-01

    Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

  6. Anomaly detection in random heterogeneous media Feynman-Kac formulae, stochastic homogenization and statistical inversion

    CERN Document Server

    Simon, Martin

    2015-01-01

    This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem.   Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems  Targe...

  7. Stochastic thermodynamics

    Science.gov (United States)

    Eichhorn, Ralf; Aurell, Erik

    2014-04-01

    theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them

  8. Stochastic volatility and stochastic leverage

    DEFF Research Database (Denmark)

    Veraart, Almut; Veraart, Luitgard A. M.

    This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

  9. Modelling and application of stochastic processes

    CERN Document Server

    1986-01-01

    The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza­ tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...

  10. Variance decomposition in stochastic simulators.

    Science.gov (United States)

    Le Maître, O P; Knio, O M; Moraes, A

    2015-06-28

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  11. Variance decomposition in stochastic simulators

    Science.gov (United States)

    Le Maître, O. P.; Knio, O. M.; Moraes, A.

    2015-06-01

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  12. Variance decomposition in stochastic simulators

    Energy Technology Data Exchange (ETDEWEB)

    Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

    2015-06-28

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  13. Variance decomposition in stochastic simulators

    KAUST Repository

    Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro

    2015-01-01

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  14. High-speed Stochastic Fatigue Testing

    DEFF Research Database (Denmark)

    Brincker, Rune; Sørensen, John Dalsgaard

    1990-01-01

    Good stochastic fatigue tests are difficult to perform. One of the major reasons is that ordinary servohydraulic loading systems realize the prescribed load history accurately at very low testing speeds only. If the speeds used for constant amplitude testing are applied to stochastic fatigue...

  15. Stochastic processes

    CERN Document Server

    Parzen, Emanuel

    1962-01-01

    Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine

  16. Stochastic quantization

    International Nuclear Information System (INIS)

    Klauder, J.R.

    1983-01-01

    The author provides an introductory survey to stochastic quantization in which he outlines this new approach for scalar fields, gauge fields, fermion fields, and condensed matter problems such as electrons in solids and the statistical mechanics of quantum spins. (Auth.)

  17. RES: Regularized Stochastic BFGS Algorithm

    Science.gov (United States)

    Mokhtari, Aryan; Ribeiro, Alejandro

    2014-12-01

    RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

  18. Stochastic Analysis : A Series of Lectures

    CERN Document Server

    Dozzi, Marco; Flandoli, Franco; Russo, Francesco

    2015-01-01

    This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...

  19. STOCHASTIC ASSESSMENT OF NIGERIAN STOCHASTIC ...

    African Journals Online (AJOL)

    eobe

    STOCHASTIC ASSESSMENT OF NIGERIAN WOOD FOR BRIDGE DECKS ... abandoned bridges with defects only in their decks in both rural and urban locations can be effectively .... which can be seen as the detection of rare physical.

  20. Realizability: a historical essay

    NARCIS (Netherlands)

    Oosten, J. van

    2000-01-01

    The purpose of this short paper is to sketch the development of a few basic topics in the history of Realizability The number of topics is quite limited and reects very much my own personal taste biases and prejudices Realizability has over the past years developed into a subject of such dimensions

  1. Realized Volatility Risk

    NARCIS (Netherlands)

    D.E. Allen (David); M.J. McAleer (Michael); M. Scharth (Marcel)

    2013-01-01

    textabstractIn this paper we document that realized variation measures constructed from highfrequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive.

  2. Asymmetric Realized Volatility Risk

    NARCIS (Netherlands)

    D.E. Allen (David); M.J. McAleer (Michael); M. Scharth (Marcel)

    2014-01-01

    markdownabstract__Abstract__ In this paper we document that realized variation measures constructed from high-frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized

  3. K-Minimax Stochastic Programming Problems

    Science.gov (United States)

    Nedeva, C.

    2007-10-01

    The purpose of this paper is a discussion of a numerical procedure based on the simplex method for stochastic optimization problems with partially known distribution functions. The convergence of this procedure is proved by the condition on dual problems.

  4. Quantum stochastics

    CERN Document Server

    Chang, Mou-Hsiung

    2015-01-01

    The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...

  5. Asymmetric Realized Volatility Risk

    Directory of Open Access Journals (Sweden)

    David E. Allen

    2014-06-01

    Full Text Available In this paper, we document that realized variation measures constructed from high-frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly Gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Explicitly modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility model, which incorporates the fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.

  6. Realized Cost Savings 2016

    Data.gov (United States)

    Department of Veterans Affairs — This dataset is provided as a requirement of OMB’s Integrated Data Collection (IDC) and links to VA’s Realized Cost Savings and Avoidances data in JSON format. Cost...

  7. Design and realization

    International Nuclear Information System (INIS)

    1986-01-01

    Most typical papers on the Ganil construction have been gathered in this book to somehow notice the success of its realization. Papers concern the accelerator and beam line, excluding experimental areas

  8. Brownian motion, martingales, and stochastic calculus

    CERN Document Server

    Le Gall, Jean-François

    2016-01-01

    This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

  9. Realized kernels in practice

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Hansen, P. Reinhard; Lunde, Asger

    2009-01-01

    and find a remarkable level of agreement. We identify some features of the high-frequency data, which are challenging for realized kernels. They are when there are local trends in the data, over periods of around 10 minutes, where the prices and quotes are driven up or down. These can be associated......Realized kernels use high-frequency data to estimate daily volatility of individual stock prices. They can be applied to either trade or quote data. Here we provide the details of how we suggest implementing them in practice. We compare the estimates based on trade and quote data for the same stock...

  10. Modeling returns volatility: Realized GARCH incorporating realized risk measure

    Science.gov (United States)

    Jiang, Wei; Ruan, Qingsong; Li, Jianfeng; Li, Ye

    2018-06-01

    This study applies realized GARCH models by introducing several risk measures of intraday returns into the measurement equation, to model the daily volatility of E-mini S&P 500 index futures returns. Besides using the conventional realized measures, realized volatility and realized kernel as our benchmarks, we also use generalized realized risk measures, realized absolute deviation, and two realized tail risk measures, realized value-at-risk and realized expected shortfall. The empirical results show that realized GARCH models using the generalized realized risk measures provide better volatility estimation for the in-sample and substantial improvement in volatility forecasting for the out-of-sample. In particular, the realized expected shortfall performs best for all of the alternative realized measures. Our empirical results reveal that future volatility may be more attributable to present losses (risk measures). The results are robust to different sample estimation windows.

  11. Stochastic processes

    CERN Document Server

    Borodin, Andrei N

    2017-01-01

    This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.

  12. Stochastic quantization and topological theories

    International Nuclear Information System (INIS)

    Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.

    1992-01-01

    In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones

  13. Optimal Control for Stochastic Delay Evolution Equations

    Energy Technology Data Exchange (ETDEWEB)

    Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)

    2016-08-15

    In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

  14. Realizing the Witch

    OpenAIRE

    Baxstrom, Richard; Meyers, Todd

    2016-01-01

    Benjamin Christensen’s Häxan (The Witch, 1922) stands as a singular film within the history of cinema. Deftly weaving contemporary scientific analysis and powerfully staged historical scenes of satanic initiation, confession under torture, possession, and persecution, Häxan creatively blends spectacle and argument to provoke a humanist re-evaluation of witchcraft in European history as well as the contemporary treatment of female “hysterics” and the mentally ill. In Realizing the Witch, Baxst...

  15. Stochastic kinetics

    International Nuclear Information System (INIS)

    Colombino, A.; Mosiello, R.; Norelli, F.; Jorio, V.M.; Pacilio, N.

    1975-01-01

    A nuclear system kinetics is formulated according to a stochastic approach. The detailed probability balance equations are written for the probability of finding the mixed population of neutrons and detected neutrons, i.e. detectrons, at a given level for a given instant of time. Equations are integrated in search of a probability profile: a series of cases is analyzed through a progressive criterium. It tends to take into account an increasing number of physical processes within the chosen model. The most important contribution is that solutions interpret analytically experimental conditions of equilibrium (moise analysis) and non equilibrium (pulsed neutron measurements, source drop technique, start up procedures)

  16. Stochastic Jeux

    Directory of Open Access Journals (Sweden)

    Romanu Ekaterini

    2006-01-01

    Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.

  17. Realization theory for rational systems: Minimal rational realizations

    NARCIS (Netherlands)

    J. Nemcová (Jana); J.H. van Schuppen (Jan)

    2010-01-01

    htmlabstractThe study of realizations of response maps is a topic of control and system theory. Realization theory is used in system identification and control synthesis. A minimal rational realization of a given response map p is a rational realization of p such that the dimension of its state

  18. Stochastic biomathematical models with applications to neuronal modeling

    CERN Document Server

    Batzel, Jerry; Ditlevsen, Susanne

    2013-01-01

    Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

  19. Concurrency in product realization

    Science.gov (United States)

    Kelly, Michael J.

    1994-03-01

    Technology per se does not provide a competitive advantage. Timely exploitation of technology is what gives the competitive edge, and this demands a major shift in the product development process and management of the industrial enterprise. `Teaming to win' is more than a management theme; it is the disciplined engineering practice that is essential to success in today's global marketplace. Teaming supports the concurrent engineering practices required to integrate the activities of people responsible for product realization through achievement of shorter development cycles, lower costs, and defect-free products.

  20. Oscillators from nonlinear realizations

    Science.gov (United States)

    Kozyrev, N.; Krivonos, S.

    2018-02-01

    We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.

  1. Strategy of VHTR Realization

    International Nuclear Information System (INIS)

    Chang, Jonghwa

    2015-01-01

    High temperature gas cooled reactor has been developed since 1956. Fundamental idea of a gas cooled reactor is to achieve high temperature which is suitable for high efficiency application such as electricity generation. The core is composed of ceramics, graphite blocks which are mechanical stable up to very high temperature. Fuel is ceramics, TRISO ( tri-isotropic coated micro particle) whose dense coating layers work as small radioactivity containment. Coolant is inert gas, helium, which is stable chemically, neutronically, and thermal hydraulically. Several test reactors such as DRE, PB-1, FSV, AVR, THTR, HTTR, HTR-10 were built and demonstrated their safety. Large GA-HTR, RSA-PBMR projects are canceled and US-NGNP project is idling. Only Chinese HTR-PM demonstrator is under construction. HTGR has long history of development. For realization and market penetration, VHTR community should look at niche market such as carbon free energy supply to industry complex, electric power for small grid, carbon free hydrogen production, power source for space colony. Technology Readiness Level should be advanced to get proper investment from industry. For this, cooperation between international R and D institutions is required. Clearly divided role between universities, research institutions, and industries will reduce complication and shorten VHTR realization day

  2. Strategy of VHTR Realization

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Jonghwa [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2015-10-15

    High temperature gas cooled reactor has been developed since 1956. Fundamental idea of a gas cooled reactor is to achieve high temperature which is suitable for high efficiency application such as electricity generation. The core is composed of ceramics, graphite blocks which are mechanical stable up to very high temperature. Fuel is ceramics, TRISO ( tri-isotropic coated micro particle) whose dense coating layers work as small radioactivity containment. Coolant is inert gas, helium, which is stable chemically, neutronically, and thermal hydraulically. Several test reactors such as DRE, PB-1, FSV, AVR, THTR, HTTR, HTR-10 were built and demonstrated their safety. Large GA-HTR, RSA-PBMR projects are canceled and US-NGNP project is idling. Only Chinese HTR-PM demonstrator is under construction. HTGR has long history of development. For realization and market penetration, VHTR community should look at niche market such as carbon free energy supply to industry complex, electric power for small grid, carbon free hydrogen production, power source for space colony. Technology Readiness Level should be advanced to get proper investment from industry. For this, cooperation between international R and D institutions is required. Clearly divided role between universities, research institutions, and industries will reduce complication and shorten VHTR realization day.

  3. Stochastic modeling

    CERN Document Server

    Lanchier, Nicolas

    2017-01-01

    Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...

  4. STOCHASTIC FLOWS OF MAPPINGS

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

  5. Stochastic Averaging and Stochastic Extremum Seeking

    CERN Document Server

    Liu, Shu-Jun

    2012-01-01

    Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...

  6. Synthetic Sediments and Stochastic Groundwater Hydrology

    Science.gov (United States)

    Wilson, J. L.

    2002-12-01

    For over twenty years the groundwater community has pursued the somewhat elusive goal of describing the effects of aquifer heterogeneity on subsurface flow and chemical transport. While small perturbation stochastic moment methods have significantly advanced theoretical understanding, why is it that stochastic applications use instead simulations of flow and transport through multiple realizations of synthetic geology? Allan Gutjahr was a principle proponent of the Fast Fourier Transform method for the synthetic generation of aquifer properties and recently explored new, more geologically sound, synthetic methods based on multi-scale Markov random fields. Focusing on sedimentary aquifers, how has the state-of-the-art of synthetic generation changed and what new developments can be expected, for example, to deal with issues like conceptual model uncertainty, the differences between measurement and modeling scales, and subgrid scale variability? What will it take to get stochastic methods, whether based on moments, multiple realizations, or some other approach, into widespread application?

  7. Topological superposition of abstractions of stochastic processes

    NARCIS (Netherlands)

    Bujorianu, L.M.; Bujorianu, M.C.

    2008-01-01

    In this paper, we present a sound integration mechanism for Markov processes that are abstractions of stochastic hybrid systems (SHS). In a previous work, we have defined a very general model of SHS and we proved that the realization of an SHS is a Markov process. Moreover, we have developed a

  8. Some recent developments in stochastic volatility modelling

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.

    2002-01-01

    This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...

  9. Experimental realization of linear-optical partial SWAP gates

    Czech Academy of Sciences Publication Activity Database

    Černoch, Antonín; Soubusta, Jan; Bartůšková, L.; Dušek, M.; Fiurášek, J.

    2008-01-01

    Roč. 100, č. 18 (2008), 180501/1-180501/4 ISSN 0031-9007 R&D Projects: GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : two-qubit gates * Mach-Zehnder interferomeret * quantum information processing Subject RIV: BH - Optics, Masers, Lasers Impact factor: 7.180, year: 2008

  10. Transport stochastic multi-dimensional media

    International Nuclear Information System (INIS)

    Haran, O.; Shvarts, D.

    1996-01-01

    Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors)

  11. Transport stochastic multi-dimensional media

    Energy Technology Data Exchange (ETDEWEB)

    Haran, O; Shvarts, D [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev; Thiberger, R [Ben-Gurion Univ. of the Negev, Beersheba (Israel)

    1996-12-01

    Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors).

  12. Invariant measures for stochastic nonlinear beam and wave equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Ondreját, Martin; Seidler, Jan

    2016-01-01

    Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf

  13. Fundamental partial compositeness

    DEFF Research Database (Denmark)

    Sannino, Francesco; Strumia, Alessandro; Tesi, Andrea

    2016-01-01

    We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Unde...

  14. Stochastic resonance

    International Nuclear Information System (INIS)

    Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas

    2004-01-01

    We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise

  15. Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control

    International Nuclear Information System (INIS)

    Masiero, Federica

    2005-01-01

    Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations

  16. Process theory for supervisory control of stochastic systems with data

    NARCIS (Netherlands)

    Markovski, J.

    2012-01-01

    We propose a process theory for supervisory control of stochastic nondeterministic plants with data-based observations. The Markovian process theory with data relies on the notion of Markovian partial bisimulation to capture controllability of stochastic nondeterministic systems. It presents a

  17. Jacobian elliptic function expansion solutions of nonlinear stochastic equations

    International Nuclear Information System (INIS)

    Wei Caimin; Xia Zunquan; Tian Naishuo

    2005-01-01

    Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

  18. Stochastic volatility models and Kelvin waves

    Energy Technology Data Exchange (ETDEWEB)

    Lipton, Alex [Merrill Lynch, Mlfc Main, 2 King Edward Street, London EC1A 1HQ (United Kingdom); Sepp, Artur [Merrill Lynch, 4 World Financial Center, New York, NY 10080 (United States)], E-mail: Alex_Lipton@ml.com, E-mail: Artur_Sepp@ml.com

    2008-08-29

    We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

  19. Stochastic volatility models and Kelvin waves

    Science.gov (United States)

    Lipton, Alex; Sepp, Artur

    2008-08-01

    We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

  20. Stochastic volatility models and Kelvin waves

    International Nuclear Information System (INIS)

    Lipton, Alex; Sepp, Artur

    2008-01-01

    We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics

  1. Stochastic global optimization as a filtering problem

    International Nuclear Information System (INIS)

    Stinis, Panos

    2012-01-01

    We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access to noisy measurements of the functions or statistical estimates provided through Monte Carlo sampling. This makes iterative optimization algorithms behave like stochastic maps. Naive global optimization amounts to evolving a collection of realizations of this stochastic map and picking the realization with the best properties. This motivates the use of filtering techniques to allow focusing on realizations that are more promising than others. In particular, we present a filtering reformulation of global optimization in terms of a special case of sequential importance sampling methods called particle filters. The increasing popularity of particle filters is based on the simplicity of their implementation and their flexibility. We utilize the flexibility of particle filters to construct a stochastic global optimization algorithm which can converge to the optimal solution appreciably faster than naive global optimization. Several examples of parametric exponential density estimation are provided to demonstrate the efficiency of the approach.

  2. Realizing Controllable Quantum States

    Science.gov (United States)

    Takayanagi, Hideaki; Nitta, Junsaku

    -- 4. Mesoscopic superconductivity with unconventional superconductor or ferromagnet. Ultraefficient microrefrigerators realized with ferromagnet-superconductor junctions / F. Giazotto et al. Anomalous charge transport in triplet superconductor junctions by the synergy effect of the proximity effect and the mid gap Andreev resonant states / Y. Tanaka and S. Kashiwaya. Paramagnetic and glass states in superconductive YBa[symbol]Cu[symbol]O[symbol] ceramics of sub-micron scale grains / H. Deguchi et al. Quantum properties of single-domain triplet superconductors / A. M. Gulian and K. S. Wood. A numerical study of Josephson current in p wave superconducting junctions / Y. Asano et al. Tilted bi-crystal sapphire substrates improve properties of grain boundary YBa[symbol]Cu[symbol]O[symbol] junctions and extend their Josephson response to THZ frequencies / E. Stepantsov et al. Circuit theory analysis of AB-plane tunnel junctions of unconventional superconductor Bi[symbol]Sr[symbol]Ca[symbol]Cu[symbol]O[symbol] / I. Shigeta et al. Transport properties of normal metal/anisotropic superconductor junctions in the eutectic system Sr[symbol]RuO[symbol]Ru / M. Kawamura et al. Macroscopic quantum tunneling in d-wave superconductor Josephson / S. Kawabata et al. Quasiparticle states of high-T[symbol] oxides observed by a Zeeman magnetic field response / S. Kashiwaya et al. Experimentally realizable devices for controlling the motion of magnetic flux quanta in anisotropic superconductors: vortex lenses, vortex diodes and vortex pumps / S. Savel'ev and F. Nori. Stability of vortex-antivortex "molecules" in mesoscopic superconducting triangles / V. R. Misko et al. Superconducting network with magnetic decoration - Hofstadter butterfly in spatially modulated magnetic field / Y. Iye et al. Observation of paramagnetic supercurrent in mesoscopic superconducting rings and disks using multiple-small-tunnel-junction method / A. Kanda et al. Guidance of vortices in high

  3. Stochastic tools in turbulence

    CERN Document Server

    Lumey, John L

    2012-01-01

    Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the

  4. Realistic Realizations Of Threshold Circuits

    Science.gov (United States)

    Razavi, Hassan M.

    1987-08-01

    Threshold logic, in which each input is weighted, has many theoretical advantages over the standard gate realization, such as reducing the number of gates, interconnections, and power dissipation. However, because of the difficult synthesis procedure and complicated circuit implementation, their use in the design of digital systems is almost nonexistant. In this study, three methods of NMOS realizations are discussed, and their advantages and shortcomings are explored. Also, the possibility of using the methods to realize multi-valued logic is examined.

  5. Algorithms over partially ordered sets

    DEFF Research Database (Denmark)

    Baer, Robert M.; Østerby, Ole

    1969-01-01

    in partially ordered sets, answer the combinatorial question of how many maximal chains might exist in a partially ordered set withn elements, and we give an algorithm for enumerating all maximal chains. We give (in § 3) algorithms which decide whether a partially ordered set is a (lower or upper) semi......-lattice, and whether a lattice has distributive, modular, and Boolean properties. Finally (in § 4) we give Algol realizations of the various algorithms....

  6. Noncausal stochastic calculus

    CERN Document Server

    Ogawa, Shigeyoshi

    2017-01-01

    This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

  7. American option pricing with stochastic volatility processes

    Directory of Open Access Journals (Sweden)

    Ping LI

    2017-12-01

    Full Text Available In order to solve the problem of option pricing more perfectly, the option pricing problem with Heston stochastic volatility model is considered. The optimal implementation boundary of American option and the conditions for its early execution are analyzed and discussed. In view of the fact that there is no analytical American option pricing formula, through the space discretization parameters, the stochastic partial differential equation satisfied by American options with Heston stochastic volatility is transformed into the corresponding differential equations, and then using high order compact finite difference method, numerical solutions are obtained for the option price. The numerical experiments are carried out to verify the theoretical results and simulation. The two kinds of optimal exercise boundaries under the conditions of the constant volatility and the stochastic volatility are compared, and the results show that the optimal exercise boundary also has stochastic volatility. Under the setting of parameters, the behavior and the nature of volatility are analyzed, the volatility curve is simulated, the calculation results of high order compact difference method are compared, and the numerical option solution is obtained, so that the method is verified. The research result provides reference for solving the problems of option pricing under stochastic volatility such as multiple underlying asset option pricing and barrier option pricing.

  8. Multiple fields in stochastic inflation

    Energy Technology Data Exchange (ETDEWEB)

    Assadullahi, Hooshyar [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Noorbala, Mahdiyar [Department of Physics, University of Tehran,P.O. Box 14395-547, Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Vennin, Vincent; Wands, David [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom)

    2016-06-24

    Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.

  9. Partially composite Higgs models

    DEFF Research Database (Denmark)

    Alanne, Tommi; Buarque Franzosi, Diogo; Frandsen, Mads T.

    2018-01-01

    We study the phenomenology of partially composite-Higgs models where electroweak symmetry breaking is dynamically induced, and the Higgs is a mixture of a composite and an elementary state. The models considered have explicit realizations in terms of gauge-Yukawa theories with new strongly...... interacting fermions coupled to elementary scalars and allow for a very SM-like Higgs state. We study constraints on their parameter spaces from vacuum stability and perturbativity as well as from LHC results and find that requiring vacuum stability up to the compositeness scale already imposes relevant...... constraints. A small part of parameter space around the classically conformal limit is stable up to the Planck scale. This is however already strongly disfavored by LHC results. in different limits, the models realize both (partially) composite-Higgs and (bosonic) technicolor models and a dynamical extension...

  10. Physical Realizations of Quantum Computing

    CERN Document Server

    Kanemitsu, Shigeru; Salomaa, Martti; Takagi, Shin; Are the DiVincenzo Criteria Fulfilled in 2004 ?

    2006-01-01

    The contributors of this volume are working at the forefront of various realizations of quantum computers. They survey the recent developments in each realization, in the context of the DiVincenzo criteria, including nuclear magnetic resonance, Josephson junctions, quantum dots, and trapped ions. There are also some theoretical contributions which have relevance in the physical realizations of a quantum computer. This book fills the gap between elementary introductions to the subject and highly specialized research papers to allow beginning graduate students to understand the cutting-edge of r

  11. A non-linear dimension reduction methodology for generating data-driven stochastic input models

    Science.gov (United States)

    Ganapathysubramanian, Baskar; Zabaras, Nicholas

    2008-06-01

    Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low

  12. A non-linear dimension reduction methodology for generating data-driven stochastic input models

    International Nuclear Information System (INIS)

    Ganapathysubramanian, Baskar; Zabaras, Nicholas

    2008-01-01

    Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R n . An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R d (d<< n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology

  13. Maximal stochastic transport in the Lorenz equations

    Energy Technology Data Exchange (ETDEWEB)

    Agarwal, Sahil, E-mail: sahil.agarwal@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: john.wettlaufer@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)

    2016-01-08

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  14. Stochastic chaos in a Duffing oscillator and its control

    International Nuclear Information System (INIS)

    Wu Cunli; Lei Youming; Fang Tong

    2006-01-01

    Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos

  15. Proposal and realization advertising campaign

    OpenAIRE

    RYCHLÁ, Marie

    2008-01-01

    The Bachelor Paper contains proposal and realization advertising campaign, including make charge for cost amount. The advertising campaign is made for chosen product of firm. Advertising campaign is planning by the medium of broadsheet and advertising on the Internet.

  16. The appreciation of stochastic motion in particle accelerators

    International Nuclear Information System (INIS)

    Symon, Keith; Sessler, Andrew

    2003-01-01

    A description is given of the analytic and numerical work, performed from July 1955 through August 1956, so as to develop, and then study, the process of making intense proton beams, suitable for colliding beams. It is shown how this investigation led, in a most natural way, to the realization that stochasticity can arise in a simple Hamiltonian system. Furthermore, the criterion for the onset of stochasticity was understood, and carefully studied, in two different situations. The first situation was the proposed (and subsequently used) ''stacking process'' for developing an intense beam, where stochasticity occurs as additional particles are added to the intense circulating beam. The second situation occurs when one seeks to develop ''stochastic accelerators'' in which particles are accelerated (continuously) by a collection of radio frequency systems. It was in the last connection that the well-known criterion for stochasticity, resonance overlap, was obtained

  17. Stochastic samples versus vacuum expectation values in cosmology

    International Nuclear Information System (INIS)

    Tsamis, N.C.; Tzetzias, Aggelos; Woodard, R.P.

    2010-01-01

    Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some things, such as the stress tensor, we argue that operators exist for which there is no essential problem. We quantify this by examining the stochastic properties of a noninteracting, massless, minimally coupled scalar on a locally de Sitter background. The square of the stochastic realization of this field seems to provide an example of great relevance for which expectation values are not misleading. We also examine the frequently expressed concern that significant back-reaction from expectation values necessarily implies large stochastic fluctuations between nearby spatial points. Rather than viewing the stochastic formalism in opposition to expectation values, we argue that it provides a marvelously simple way of capturing the leading infrared logarithm corrections to the latter, as advocated by Starobinsky

  18. Stochastic resonance: noise-enhanced order

    International Nuclear Information System (INIS)

    Anishchenko, Vadim S; Neiman, Arkady B; Moss, F; Shimansky-Geier, L

    1999-01-01

    Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. (reviews of topical problems)

  19. Stochastic resonance: noise-enhanced order

    Energy Technology Data Exchange (ETDEWEB)

    Anishchenko, Vadim S; Neiman, Arkady B [N.G. Chernyshevskii Saratov State University, Saratov (Russian Federation); Moss, F [Department of Physics and Astronomy, University of Missouri at St. Louis (United States); Shimansky-Geier, L [Humboldt University at Berlin (Germany)

    1999-01-31

    Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. (reviews of topical problems)

  20. Elitism and Stochastic Dominance

    OpenAIRE

    Bazen, Stephen; Moyes, Patrick

    2011-01-01

    Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the...

  1. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  2. Computational stochastic model of ions implantation

    Energy Technology Data Exchange (ETDEWEB)

    Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)

    2015-03-10

    Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

  3. Lectures on Topics in Spatial Stochastic Processes

    CERN Document Server

    Capasso, Vincenzo; Ivanoff, B Gail; Dozzi, Marco; Dalang, Robert C; Mountford, Thomas S

    2003-01-01

    The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

  4. Stochastic control with rough paths

    International Nuclear Information System (INIS)

    Diehl, Joscha; Friz, Peter K.; Gassiat, Paul

    2017-01-01

    We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).

  5. Stochastic control with rough paths

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)

    2017-04-15

    We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).

  6. Stochastic analytic regularization

    International Nuclear Information System (INIS)

    Alfaro, J.

    1984-07-01

    Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)

  7. Instantaneous stochastic perturbation theory

    International Nuclear Information System (INIS)

    Lüscher, Martin

    2015-01-01

    A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

  8. Stochastic climate theory

    NARCIS (Netherlands)

    Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.

    2017-01-01

    In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of

  9. On Stochastic Dependence

    Science.gov (United States)

    Meyer, Joerg M.

    2018-01-01

    The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.

  10. Stochastic quantization and gravity

    International Nuclear Information System (INIS)

    Rumpf, H.

    1984-01-01

    We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)

  11. Stochastic neuron models

    CERN Document Server

    Greenwood, Priscilla E

    2016-01-01

    This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...

  12. Backward stochastic differential equations from linear to fully nonlinear theory

    CERN Document Server

    Zhang, Jianfeng

    2017-01-01

    This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

  13. Stochastic calculus an introduction through theory and exercises

    CERN Document Server

    Baldi, Paolo

    2017-01-01

    This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical ...

  14. Multiple Realizability and Biological Laws

    NARCIS (Netherlands)

    Raerinne, Jani P.; Eronen, Markus I.

    2012-01-01

    We critically analyze Alexander Rosenberg's argument based on the multiple realizability of biological properties that there are no biological laws. The argument is intuitive and suggestive. Nevertheless, a closer analysis reveals that the argument rests on dubious assumptions about the nature of

  15. Realizations of the canonical representation

    Indian Academy of Sciences (India)

    Traditionally, the canonical representation is realized on the Hilbert space ... Fix a decomposition R2n = Rn × Rn ..... to an orthonormal basis {ψ1,ψ2,. ..... [7] Vemuri M K, A non-commutative Sobolev inequality and its application to spectral.

  16. Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance

    NARCIS (Netherlands)

    M. Asai (Manabu); M.J. McAleer (Michael)

    2014-01-01

    markdownabstract__Abstract__ Modelling covariance structures is known to suffer from the curse of dimensionality. In order to avoid this problem for forecasting, the authors propose a new factor multivariate stochastic volatility (fMSV) model for realized covariance measures that accommodates

  17. A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

    Energy Technology Data Exchange (ETDEWEB)

    Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)

    2012-12-15

    We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

  18. A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

    International Nuclear Information System (INIS)

    Hosking, John Joseph Absalom

    2012-01-01

    We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966–979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197–216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

  19. Sequential stochastic optimization

    CERN Document Server

    Cairoli, Renzo

    1996-01-01

    Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet

  20. Remarks on stochastic acceleration

    International Nuclear Information System (INIS)

    Graeff, P.

    1982-12-01

    Stochastic acceleration and turbulent diffusion are strong turbulence problems since no expansion parameter exists. Hence the problem of finding rigorous results is of major interest both for checking approximations and for reference models. Since we have found a way of constructing such models in the turbulent diffusion case the question of the extension to stochastic acceleration now arises. The paper offers some possibilities illustrated by the case of 'stochastic free fall' which may be particularly interesting in the context of linear response theory. (orig.)

  1. PRAGMATIC TRANSFER IN REQUEST REALIZATIONS

    Directory of Open Access Journals (Sweden)

    Indawan Syahri

    2007-01-01

    Full Text Available This study investigates the pragmatic transfer in English request realizations made by EFL learners, i.e. the proficient learners. The subjects were students of an English Study Program who obtained TOEFL-like scores of at least 450. The data were collected by means of DCT-questionnaires and Role-plays. The results show that the subjects realize requests in the form of external modifications more frequently. Most of them embed their requests with supportive moves dominantly. They enfold the acts with the moves before, after or in both positions. Of the three positions, they mostly insert the moves initial position, i.e., through inductive patterns. This is due to pragmatic transfer.

  2. A Stochastic Model for Malaria Transmission Dynamics

    Directory of Open Access Journals (Sweden)

    Rachel Waema Mbogo

    2018-01-01

    Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

  3. The interpolation method of stochastic functions and the stochastic variational principle

    International Nuclear Information System (INIS)

    Liu Xianbin; Chen Qiu

    1993-01-01

    Uncertainties have been attaching more importance to increasingly in modern engineering structural design. Viewed on an appropriate scale, the inherent physical attributes (material properties) of many structural systems always exhibit some patterns of random variation in space and time, generally the random variation shows a small parameter fluctuation. For a linear mechanical system, the random variation is modeled as a random one of a linear partial differential operator and, in stochastic finite element method, a random variation of a stiffness matrix. Besides the stochasticity of the structural physical properties, the influences of random loads which always represent themselves as the random boundary conditions bring about much more complexities in structural analysis. Now the stochastic finite element method or the probabilistic finite element method is used to study the structural systems with random physical parameters, whether or not the loads are random. Differing from the general finite element theory, the main difficulty which the stochastic finite element method faces is the inverse operation of stochastic operators and stochastic matrices, since the inverse operators and the inverse matrices are statistically correlated to the random parameters and random loads. So far, many efforts have been made to obtain the reasonably approximate expressions of the inverse operators and inverse matrices, such as Perturbation Method, Neumann Expansion Method, Galerkin Method (in appropriate Hilbert Spaces defined for random functions), Orthogonal Expansion Method. Among these methods, Perturbation Method appear to be the most available. The advantage of these methods is that the fairly accurate response statistics can be obtained under the condition of the finite information of the input. However, the second-order statistics obtained by use of Perturbation Method and Neumann Expansion Method are not always the appropriate ones, because the relevant second

  4. [Posterior ceramic bonded partial restorations].

    Science.gov (United States)

    Mainjot, Amélie; Vanheusden, Alain

    2006-01-01

    Posterior ceramic bonded partial restorations are conservative and esthetic approaches for compromised teeth. Overlays constitute a less invasive alternative for tooth tissues than crown preparations. With inlays and onlays they are also indicated in case of full arch or quadrant rehabilitations including several teeth. This article screens indications and realization of this type of restorations.

  5. Stochastic models for tumoral growth

    Science.gov (United States)

    Escudero, Carlos

    2006-02-01

    Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.

  6. Stochastic processes inference theory

    CERN Document Server

    Rao, Malempati M

    2014-01-01

    This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.

  7. Introduction to stochastic calculus

    CERN Document Server

    Karandikar, Rajeeva L

    2018-01-01

    This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...

  8. Stochastic coalgebraic logic

    CERN Document Server

    Doberkat, Ernst-Erich

    2009-01-01

    Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.

  9. Stochastic learning in oxide binary synaptic device for neuromorphic computing.

    Science.gov (United States)

    Yu, Shimeng; Gao, Bin; Fang, Zheng; Yu, Hongyu; Kang, Jinfeng; Wong, H-S Philip

    2013-01-01

    Hardware implementation of neuromorphic computing is attractive as a computing paradigm beyond the conventional digital computing. In this work, we show that the SET (off-to-on) transition of metal oxide resistive switching memory becomes probabilistic under a weak programming condition. The switching variability of the binary synaptic device implements a stochastic learning rule. Such stochastic SET transition was statistically measured and modeled for a simulation of a winner-take-all network for competitive learning. The simulation illustrates that with such stochastic learning, the orientation classification function of input patterns can be effectively realized. The system performance metrics were compared between the conventional approach using the analog synapse and the approach in this work that employs the binary synapse utilizing the stochastic learning. The feasibility of using binary synapse in the neurormorphic computing may relax the constraints to engineer continuous multilevel intermediate states and widens the material choice for the synaptic device design.

  10. Approximating Preemptive Stochastic Scheduling

    OpenAIRE

    Megow Nicole; Vredeveld Tjark

    2009-01-01

    We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

  11. The stochastic goodwill problem

    OpenAIRE

    Marinelli, Carlo

    2003-01-01

    Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionar...

  12. BRST stochastic quantization

    International Nuclear Information System (INIS)

    Hueffel, H.

    1990-01-01

    After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)

  13. Stochastic Modeling of Past Volcanic Crises

    Science.gov (United States)

    Woo, Gordon

    2018-01-01

    The statistical foundation of disaster risk analysis is past experience. From a scientific perspective, history is just one realization of what might have happened, given the randomness and chaotic dynamics of Nature. Stochastic analysis of the past is an exploratory exercise in counterfactual history, considering alternative possible scenarios. In particular, the dynamic perturbations that might have transitioned a volcano from an unrest to an eruptive state need to be considered. The stochastic modeling of past volcanic crises leads to estimates of eruption probability that can illuminate historical volcanic crisis decisions. It can also inform future economic risk management decisions in regions where there has been some volcanic unrest, but no actual eruption for at least hundreds of years. Furthermore, the availability of a library of past eruption probabilities would provide benchmark support for estimates of eruption probability in future volcanic crises.

  14. Spreading paths in partially observed social networks

    Science.gov (United States)

    Onnela, Jukka-Pekka; Christakis, Nicholas A.

    2012-03-01

    Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.

  15. Spreading paths in partially observed social networks.

    Science.gov (United States)

    Onnela, Jukka-Pekka; Christakis, Nicholas A

    2012-03-01

    Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.

  16. Design and realization of simulators

    International Nuclear Information System (INIS)

    Mathey, C.

    1984-01-01

    The two main categories of simulators are training simulators of which aim is the education of the nuclear power plant operators, and the study simulators. The French park of simulators is reviewed, as also their field of utilization. One deals with the simulator design: general description, calculation tools, middleware, and programming, mathematical models and numerical methods. Then, the instructor post of the EDF's simulators are more particularly described. The realization of a simulator includes two main stages: the development of the material and, the development of the software [fr

  17. PREFACE: Nanospintronics design and realization

    Science.gov (United States)

    Akai, Hisazumi; Katayama-Yoshida, Hiroshi; Kasai, Hideaki

    2004-12-01

    This special issue of Journal of Physics: Condensed Matter contains selected papers from the 1st International Conference on Nanospintronics Design and Realization (ICNDR 2004), which was held in Kyoto, Japan, 24--28 May 2004. This conference was organized by the Nanospintronics Design and Realization project members: Hideaki Kasai, Osaka (Chair of the Conference) Hisazumi Akai, Osaka Hajime Asahi, Osaka Wilson Agerico Diño, Osaka Hiroshi Harima, Kyoto Tomoyuki Kakeshita, Osaka Junjiro Kanamori, Kyoto Hiroshi Katayama-Yoshida, Osaka Koichi Kusakabe, Osaka Hiroshi Nakanishi, Osaka (Secretary) Tamio Oguchi, Hiroshima Teruo Ono, Osaka Naoshi Suzuki, Osaka Hitoshi Tabata, Osaka under the auspices of the Japan Ministry of Education, Culture, Sports, Science and Technology (MEXT) Special Coordination Funds for Promoting Science and Technology, and the sponsorship of Osaka University and the International Institute for Advanced Studies (IIAS). The conference is intended to provide an international forum for experimental and theoretical researchers, in the rapidly developing field of nanospintronics. It aims to: provide an overview of our current understanding of the physics of spin transport in (magnetic) semiconductors and hybrid magnetic/semiconductor structures; provide a venue to present and discuss the latest developments in using spin-dependent phenomena in nano-(opto-) electronics and computing applications; provide a venue for discussion and assessment of other possible means of exploiting the spin-dependent phenomena in future nano-(opto-) electronic and computing applications; address current (and foreseeable future) problems, of fundamental and applied nature, in an effort to bridge the physics and technology gap between semiconducting and magnetic materials. All of these being geared towards bringing about the realization of a functioning nanospintronics. A total of 127 delegates from 15 countries took part in ICNDR 2004, which was comprised of 62 invited

  18. Stability analysis for neutral stochastic differential equation of second order driven by Poisson jumps

    Science.gov (United States)

    Chadha, Alka; Bora, Swaroop Nandan

    2017-11-01

    This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.

  19. New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation

    International Nuclear Information System (INIS)

    Ray, S. Saha; Singh, S.

    2017-01-01

    In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space. (paper)

  20. Achieving control and synchronization merely through a stochastically adaptive feedback coupling

    Science.gov (United States)

    Lin, Wei; Chen, Xin; Zhou, Shijie

    2017-07-01

    Techniques of deterministically adaptive feedback couplings have been successfully and extensively applied to realize control or/and synchronization in chaotic dynamical systems and even in complex dynamical networks. In this article, a technique of stochastically adaptive feedback coupling is novelly proposed to not only realize control in chaotic dynamical systems but also achieve synchronization in unidirectionally coupled systems. Compared with those deterministically adaptive couplings, the proposed stochastic technique interestingly shows some advantages from a physical viewpoint of time and energy consumptions. More significantly, the usefulness of the proposed stochastic technique is analytically validated by the theory of stochastic processes. It is anticipated that the proposed stochastic technique will be widely used in achieving system control and network synchronization.

  1. Partial Cancellation

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Partial Cancellation. Full Cancellation is desirable. But complexity requirements are enormous. 4000 tones, 100 Users billions of flops !!! Main Idea: Challenge: To determine which cross-talker to cancel on what “tone” for a given victim. Constraint: Total complexity is ...

  2. Diffusion with intrinsic trapping in 2-d incompressible stochastic velocity fields

    International Nuclear Information System (INIS)

    Vlad, M.; Spineanu, F.; Misguich, J.H.; Vlad, M.; Spineanu, F.; Balescu, R.

    1998-10-01

    A new statistical approach that applies to the high Kubo number regimes for particle diffusion in stochastic velocity fields is presented. This 2-dimensional model describes the partial trapping of the particles in the stochastic field. the results are close to the numerical simulations and also to the estimations based on percolation theory. (authors)

  3. Stochastic Differential Equations and Kondratiev Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Vaage, G.

    1995-05-01

    The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.

  4. Dreams, Perception, and Creative Realization.

    Science.gov (United States)

    Glaskin, Katie

    2015-10-01

    This article draws on the ethnography of Aboriginal Australia to argue that perceptual openness, extending from waking life into dreaming experience, provides an important cognitive framework for the apprehension of dreamt experience in these contexts. I argue that this perceptual openness is analogous to the "openness to experience" described as a personality trait that had been linked with dream recall frequency (among other things). An implication of identifying perceptual openness at a cultural rather than at an individual level is two-fold. It provides an example of the ways in which cultural differences affect perception, indicative of cognitive diversity; and, given the relationship between dreams and creativity suggested anecdotally and through research, a cultural orientation toward perceptual openness is also likely to have implications for the realization of creativity that occurs through dreams. Such creativity though cannot be separated from the relational context in which such dreamt material is elaborated and understood. Copyright © 2015 Cognitive Science Society, Inc.

  5. Periodic solutions of Wick-type stochastic Korteweg–de Vries ...

    Indian Academy of Sciences (India)

    2016-09-20

    Sep 20, 2016 ... 2Department of Applied Mathematics, Kyung Hee University, Yongin 446-701, Republic of Korea. ∗ ... Abstract. Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering.

  6. A hybrid POMDP-BDI agent architecture with online stochastic planning and plan caching

    CSIR Research Space (South Africa)

    Moodley, D

    2016-12-01

    Full Text Available This article presents an agent architecture for controlling an autonomous agent in stochastic, noisy environments. The architecture combines the partially observable Markov decision process (POMDP) model with the belief-desire-intention (BDI...

  7. Stochastic integration by parts and functional Itô calculus

    CERN Document Server

    Vives, Josep

    2016-01-01

    This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...

  8. Partial observation control in an anticipating environment

    International Nuclear Information System (INIS)

    Oeksendal, B; Sulem, A

    2004-01-01

    A study is made of a controlled stochastic system whose state X(t) at time t is described by a stochastic differential equation driven by Levy processes with filtration {F t } telementof[0,T] . The system is assumed to be anticipating, in the sense that the coefficients are assumed to be adapted to a filtration {G t } t≥0 with F t subset of equal G t for all t element of [0,T]. The corresponding anticipating stochastic differential equation is interpreted in the sense of forward integrals, which naturally generalize semimartingale integrals. The admissible controls are assumed to be adapted to a filtration {E t } telementof[0,T] such that E t subset of equal F t for all t element of [0,T]. The general problem is to maximize a given performance functional of this system over all admissible controls. This is a partial observation stochastic control problem in an anticipating environment. Examples of applications include stochastic volatity models in finance, insider influenced financial markets, and stochastic control of systems with delayed noise effects. Some particular cases in finance, involving optimal portfolios with logarithmic utility, are solved explicitly

  9. Stochastic approach to microphysics

    Energy Technology Data Exchange (ETDEWEB)

    Aron, J.C.

    1987-01-01

    The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e/sup +/e/sup -/ collisions, or pp -> ..pi../sup 0/ + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...).

  10. Stochastic dynamics and irreversibility

    CERN Document Server

    Tomé, Tânia

    2015-01-01

    This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...

  11. Stochastic optimization methods

    CERN Document Server

    Marti, Kurt

    2005-01-01

    Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

  12. Stochastic quantum gravity

    International Nuclear Information System (INIS)

    Rumpf, H.

    1987-01-01

    We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)

  13. Separable quadratic stochastic operators

    International Nuclear Information System (INIS)

    Rozikov, U.A.; Nazir, S.

    2009-04-01

    We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

  14. Stochastic cooling at Fermilab

    International Nuclear Information System (INIS)

    Marriner, J.

    1986-08-01

    The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system

  15. Partial processing

    International Nuclear Information System (INIS)

    1978-11-01

    This discussion paper considers the possibility of applying to the recycle of plutonium in thermal reactors a particular method of partial processing based on the PUREX process but named CIVEX to emphasise the differences. The CIVEX process is based primarily on the retention of short-lived fission products. The paper suggests: (1) the recycle of fission products with uranium and plutonium in thermal reactor fuel would be technically feasible; (2) it would, however, take ten years or more to develop the CIVEX process to the point where it could be launched on a commercial scale; (3) since the majority of spent fuel to be reprocessed this century will have been in storage for ten years or more, the recycling of short-lived fission products with the U-Pu would not provide an effective means of making refabrication fuel ''inaccessible'' because the radioactivity associated with the fission products would have decayed. There would therefore be no advantage in partial processing

  16. Partial gigantism

    Directory of Open Access Journals (Sweden)

    М.М. Karimova

    2017-05-01

    Full Text Available A girl with partial gigantism (the increased I and II fingers of the left foot is being examined. This condition is a rare and unresolved problem, as the definite reason of its development is not determined. Wait-and-see strategy is recommended, as well as correcting operations after closing of growth zones, and forming of data pool for generalization and development of schemes of drug and radial therapeutic methods.

  17. Parameter estimation in stochastic differential equations

    CERN Document Server

    Bishwal, Jaya P N

    2008-01-01

    Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.

  18. Dynamic optimization deterministic and stochastic models

    CERN Document Server

    Hinderer, Karl; Stieglitz, Michael

    2016-01-01

    This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.

  19. Stochastic Feedforward Control Technique

    Science.gov (United States)

    Halyo, Nesim

    1990-01-01

    Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.

  20. Markov stochasticity coordinates

    International Nuclear Information System (INIS)

    Eliazar, Iddo

    2017-01-01

    Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

  1. Stochastic Switching Dynamics

    DEFF Research Database (Denmark)

    Simonsen, Maria

    This thesis treats stochastic systems with switching dynamics. Models with these characteristics are studied from several perspectives. Initially in a simple framework given in the form of stochastic differential equations and, later, in an extended form which fits into the framework of sliding...... mode control. It is investigated how to understand and interpret solutions to models of switched systems, which are exposed to discontinuous dynamics and uncertainties (primarily) in the form of white noise. The goal is to gain knowledge about the performance of the system by interpreting the solution...

  2. Stochastic dynamics and control

    CERN Document Server

    Sun, Jian-Qiao; Zaslavsky, George

    2006-01-01

    This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc

  3. Stochastic singular optics

    CSIR Research Space (South Africa)

    Roux, FS

    2013-09-01

    Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...

  4. Foundations of stochastic analysis

    CERN Document Server

    Rao, M M; Lukacs, E

    1981-01-01

    Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea

  5. Markov stochasticity coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

    2017-01-15

    Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

  6. Stochastic integration in Banach spaces theory and applications

    CERN Document Server

    Mandrekar, Vidyadhar

    2015-01-01

    Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...

  7. Stochastic models, estimation, and control

    CERN Document Server

    Maybeck, Peter S

    1982-01-01

    This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.

  8. Some Considerations on the Partial Credit Model

    Directory of Open Access Journals (Sweden)

    H.H.F.M. Verstralen

    2008-01-01

    Full Text Available The Partial Credit Model (PCM is sometimes interpreted as a model for stepwise solution of polytomously scored items, where the item parameters are interpreted as di culties of the steps. It is argued that this interpretation is not justi ed. A model for stepwise solution is discussed. It is shown that the PCM is suited to model sums of binary responses which are not supposed to be stochastically independent. As a practical result, a statistical test of stochastic independence in the Rasch model is derived

  9. Stochastic quantisation: theme and variation

    International Nuclear Information System (INIS)

    Klauder, J.R.; Kyoto Univ.

    1987-01-01

    The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)

  10. Stochastic Simulation Using @ Risk for Dairy Business Investment Decisions

    Science.gov (United States)

    A dynamic, stochastic, mechanistic simulation model of a dairy business was developed to evaluate the cost and benefit streams coinciding with technology investments. The model was constructed to embody the biological and economical complexities of a dairy farm system within a partial budgeting fram...

  11. Constructive role of Brownian motion: Brownian motors and Stochastic Resonance

    Science.gov (United States)

    Hänggi, Peter

    2005-03-01

    Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance [1] and Brownian motors [2], however, stochastic noise can play a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Brownian motion assisted Stochastic Resonance finds useful applications in physical, technological, biological and biomedical contexts [1,3]. The basic principles that underpin Stochastic Resonance are elucidated and novel applications for nonlinear classical and quantum systems will be addressed. The presence of non-equilibrium disturbances enables to rectify Brownian motion so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems (Brownian motors). In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations are discussed [2,4,5]. [1] L. Gammaitoni, P. Hä'nggi, P. Jung and F. Marchesoni, Stochastic Resonance, Rev. Mod. Phys. 70, 223 (1998).[2] R. D. Astumian and P. Hä'nggi, Brownian motors, Physics Today 55 (11), 33 (2002).[3] P. Hä'nggi, Stochastic Resonace in Physics and Biology, ChemPhysChem 3, 285 (2002).[4] H. Linke, editor, Special Issue on Brownian Motors, Applied Physics A 75, No. 2 (2002).[5] P. Hä'nggi, F. Marchesoni, F. Nori, Brownian motors, Ann. Physik (Leipzig) 14, xxx (2004); cond-mat/0410033.

  12. Stochastic quantization of Proca field

    International Nuclear Information System (INIS)

    Lim, S.C.

    1981-03-01

    We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)

  13. Stochastic Estimation via Polynomial Chaos

    Science.gov (United States)

    2015-10-01

    AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

  14. A Realization Approach for Residual Expressions

    DEFF Research Database (Denmark)

    Skovmose Kallesøe, Carsten; Izadi-Zamanabadi, Roozbeh; Wisniewski, Rafal

    2006-01-01

    This paper is concerned with state space realization of inherent redundant information in subsystems, which are identified by structural analysis (SA) approach. The identified subsystems are assumed to involve algebraic variables, representing unknown signals. The proposed realization method...

  15. Realization of an integral using anticommuting variables

    International Nuclear Information System (INIS)

    Valuev, B.N.

    1979-01-01

    It is shown that the integral defined by Berezin over anticommuting variables may be realized as a trace on the Clifford algebra. In fact, this realization makes precise the definition of the integral

  16. Elementary stochastic cooling

    Energy Technology Data Exchange (ETDEWEB)

    Tollestrup, A.V.; Dugan, G

    1983-12-01

    Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)

  17. Affine stochastic mortality

    NARCIS (Netherlands)

    Schrager, D.F.

    2006-01-01

    We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing

  18. Composite stochastic processes

    NARCIS (Netherlands)

    Kampen, N.G. van

    Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This

  19. Entropy Production in Stochastics

    Directory of Open Access Journals (Sweden)

    Demetris Koutsoyiannis

    2017-10-01

    Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.

  20. Stochastic modelling of turbulence

    DEFF Research Database (Denmark)

    Sørensen, Emil Hedevang Lohse

    previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...

  1. Research in Stochastic Processes.

    Science.gov (United States)

    1982-10-31

    Office of Scientific Research Grant AFOSR F49620 82 C 0009 Period: 1 Noveber 1981 through 31 October 1982 Title: Research in Stochastic Processes Co...STA4ATIS CAMBANIS The work briefly described here was developed in connection with problems arising from and related to the statistical comunication

  2. Stochastic Control - External Models

    DEFF Research Database (Denmark)

    Poulsen, Niels Kjølstad

    2005-01-01

    This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...

  3. Stochastic nonlinear beam equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan

    2005-01-01

    Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005

  4. Fast Numerical Methods for Stochastic Partial Differential Equations

    Science.gov (United States)

    2016-04-15

    Particle Swarm Optimization (PSO) method. Inspired by the social behavior of the bird flocking or fish schooling, the particle swarm optimization (PSO...Weerasinghe, Hongmei Chi and Yanzhao Cao, Particle Swarm Optimization Simulation via Optimal Halton Sequences, accepted by Procedia Computer Science (2016...Optimization Simulation via Optimal Halton Sequences, accepted by Procedia Computer Science (2016). 2. Haiyan Tian, Hongmei Chi and Yanzhao Cao

  5. Primitive recursive realizability and basic propositional logic

    NARCIS (Netherlands)

    Plisko, Valery

    2007-01-01

    Two notions of primitive recursive realizability for arithmetic sentences are considered. The first one is strictly primitive recursive realizability introduced by Z. Damnjanovic in 1994. We prove that intuitionistic predicate logic is not sound with this kind of realizability. Namely there

  6. Classical realizability in the CPS target language

    DEFF Research Database (Denmark)

    Frey, Jonas

    2016-01-01

    Motivated by considerations about Krivine's classical realizability, we introduce a term calculus for an intuitionistic logic with record types, which we call the CPS target language. We give a reformulation of the constructions of classical realizability in this language, using the categorical...... techniques of realizability triposes and toposes. We argue that the presentation of classical realizability in the CPS target language simplifies calculations in realizability toposes, in particular it admits a nice presentation of conjunction as intersection type which is inspired by Girard's ludics....

  7. Explicit field realizations of W algebras

    International Nuclear Information System (INIS)

    Wei Shaowen; Liu Yuxiao; Ren Jirong; Zhang Lijie

    2009-01-01

    The fact that certain nonlinear W 2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W 2,s algebras from linear W 1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W 1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W 2,s algebras are presented. The results show that all these realizations are Romans-type realizations.

  8. Explicit field realizations of W algebras

    OpenAIRE

    Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong

    2009-01-01

    The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the explicit field realizations of linear $W_{1,2,s}$ algebras with double-scalar and double-spinor, respectively. Then, after a change of basis, the realizations of $W_{2,s}$ algebras are presented. The results show that all these realizations are Romans-type realiz...

  9. Stochastic processes in cell biology

    CERN Document Server

    Bressloff, Paul C

    2014-01-01

    This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

  10. Fundamental partial compositeness

    CERN Document Server

    Sannino, Francesco

    2016-11-07

    We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Successful models exist because gauge quantum numbers of Standard Model fermions admit a minimal enough 'square root'. Furthermore, right-handed SM fermions have an SU(2)$_R$-like structure, yielding a custodially-protected composite Higgs. Baryon and lepton numbers arise accidentally. Standard Model fermions acquire mass at tree level, while the Higgs potential and flavor violations are generated by quantum corrections. We further discuss accidental symmetries and other dynamical features stemming from the new strongly interacting scalars. If the same phenomenology can be obtained from models without our elementary scalars, they would reappear as composite states.

  11. Fundamental partial compositeness

    International Nuclear Information System (INIS)

    Sannino, Francesco; Strumia, Alessandro; Tesi, Andrea; Vigiani, Elena

    2016-01-01

    We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Under certain assumptions on the dynamics of the scalars, successful models exist because gauge quantum numbers of Standard Model fermions admit a minimal enough ‘square root’. Furthermore, right-handed SM fermions have an SU(2)_R-like structure, yielding a custodially-protected composite Higgs. Baryon and lepton numbers arise accidentally. Standard Model fermions acquire mass at tree level, while the Higgs potential and flavor violations are generated by quantum corrections. We further discuss accidental symmetries and other dynamical features stemming from the new strongly interacting scalars. If the same phenomenology can be obtained from models without our elementary scalars, they would reappear as composite states.

  12. A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects

    DEFF Research Database (Denmark)

    Bollerslev, Tim; Kretschmer, Uta; Pigorsch, Christian

    We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday...... dependencies inherent in the high-frequency intraday data....

  13. Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities

    DEFF Research Database (Denmark)

    Bollerslev, Tim; Gibson, Michael; Zhou, Hao

    experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn...

  14. Bidirectional Classical Stochastic Processes with Measurements and Feedback

    Science.gov (United States)

    Hahne, G. E.

    2005-01-01

    A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

  15. Symbolic Computing in Probabilistic and Stochastic Analysis

    Directory of Open Access Journals (Sweden)

    Kamiński Marcin

    2015-12-01

    Full Text Available The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i analytical derivations, (ii the classical Monte-Carlo simulation approach, (iii the stochastic perturbation technique, as well as (iv some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.

  16. Stochastic calculus and applications

    CERN Document Server

    Cohen, Samuel N

    2015-01-01

    Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...

  17. Some illustrations of stochasticity

    International Nuclear Information System (INIS)

    Laslett, L.J.

    1977-01-01

    A complex, and apparently stochastic, character frequently can be seen to occur in the solutions to simple Hamiltonian problems. Such behavior is of interest, and potentially of importance, to designers of particle accelerators--as well as to workers in other fields of physics and related disciplines. Even a slow development of disorder in the motion of particles in a circular accelerator or storage ring could be troublesome, because a practical design requires the beam particles to remain confined in an orderly manner within a narrow beam tube for literally tens of billions of revolutions. The material presented is primarily the result of computer calculations made to investigate the occurrence of ''stochasticity,'' and is organized in a manner similar to that adopted for presentation at a 1974 accelerator conference

  18. Stochastic ice stream dynamics.

    Science.gov (United States)

    Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca

    2016-08-09

    Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.

  19. Fractional Stochastic Field Theory

    Science.gov (United States)

    Honkonen, Juha

    2018-02-01

    Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

  20. Essentials of stochastic processes

    CERN Document Server

    Durrett, Richard

    2016-01-01

    Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...

  1. Dynamic stochastic optimization

    CERN Document Server

    Ermoliev, Yuri; Pflug, Georg

    2004-01-01

    Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic­ itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec­ tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci­ sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu­ tions. Objective an...

  2. Stochastic porous media equations

    CERN Document Server

    Barbu, Viorel; Röckner, Michael

    2016-01-01

    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  3. Stochastic stacking without filters

    International Nuclear Information System (INIS)

    Johnson, R.P.; Marriner, J.

    1982-12-01

    The rate of accumulation of antiprotons is a critical factor in the design of p anti p colliders. A design of a system to accumulate higher anti p fluxes is presented here which is an alternative to the schemes used at the CERN AA and in the Fermilab Tevatron I design. Contrary to these stacking schemes, which use a system of notch filters to protect the dense core of antiprotons from the high power of the stack tail stochastic cooling, an eddy current shutter is used to protect the core in the region of the stack tail cooling kicker. Without filters one can have larger cooling bandwidths, better mixing for stochastic cooling, and easier operational criteria for the power amplifiers. In the case considered here a flux of 1.4 x 10 8 per sec is achieved with a 4 to 8 GHz bandwidth

  4. Multistage stochastic optimization

    CERN Document Server

    Pflug, Georg Ch

    2014-01-01

    Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization.  It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book

  5. Dynamics of stochastic systems

    CERN Document Server

    Klyatskin, Valery I

    2005-01-01

    Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...

  6. Identifiability in stochastic models

    CERN Document Server

    1992-01-01

    The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.

  7. Stochastic split determinant algorithms

    International Nuclear Information System (INIS)

    Horvatha, Ivan

    2000-01-01

    I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algorithms of practical relevance might be based on Markov processes so constructed

  8. Stochasticity Modeling in Memristors

    KAUST Repository

    Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.

    2015-01-01

    Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

  9. Stochasticity Modeling in Memristors

    KAUST Repository

    Naous, Rawan

    2015-10-26

    Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

  10. Stochastic quantization of instantons

    International Nuclear Information System (INIS)

    Grandati, Y.; Berard, A.; Grange, P.

    1996-01-01

    The method of Parisi and Wu to quantize classical fields is applied to instanton solutions var-phi I of euclidian non-linear theory in one dimension. The solution var-phi var-epsilon of the corresponding Langevin equation is built through a singular perturbative expansion in var-epsilon=h 1/2 in the frame of the center of the mass of the instanton, where the difference var-phi var-epsilon -var-phi I carries only fluctuations of the instanton form. The relevance of the method is shown for the stochastic K dV equation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, the authors obtain explicit expressions for the first two orders in var-epsilon of the pertrubed instanton of its Green function. Specializing to the Sine-Gordon and var-phi 4 models, the first anaharmonic correction is obtained analytically. The calculation is carried to second order for the var-phi 4 model, showing good convergence. 21 refs., 5 fig

  11. Stochastic resonance based on modulation instability in spatiotemporal chaos.

    Science.gov (United States)

    Han, Jing; Liu, Hongjun; Huang, Nan; Wang, Zhaolu

    2017-04-03

    A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.

  12. Methods and models in mathematical biology deterministic and stochastic approaches

    CERN Document Server

    Müller, Johannes

    2015-01-01

    This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

  13. Polarization of the vacuum by a stochastic external field

    International Nuclear Information System (INIS)

    Krive, I.V.; Pastur, L.A.; Rozhavskii, A.S.

    1988-01-01

    The effect of disorder, realized in the form of a fluctuating extra mass term, on the bosonic vacuum and fermionic vacuum of models of quantum field theory is studied. A method is developed for calculating the mean effective potential in the stochastic external field. For a model of interacting scalar and fermion fields in (3+1)-dimensional space-time it is shown that random fluctuations of the mass lead to an increase of the equilibrium mean scalar field in the system

  14. Stochastic and non-stochastic effects - a conceptual analysis

    International Nuclear Information System (INIS)

    Karhausen, L.R.

    1980-01-01

    The attempt to divide radiation effects into stochastic and non-stochastic effects is discussed. It is argued that radiation or toxicological effects are contingently related to radiation or chemical exposure. Biological effects in general can be described by general laws but these laws never represent a necessary connection. Actually stochastic effects express contingent, or empirical, connections while non-stochastic effects represent semantic and non-factual connections. These two expressions stem from two different levels of discourse. The consequence of this analysis for radiation biology and radiation protection is discussed. (author)

  15. Partially composite Goldstone Higgs boson

    DEFF Research Database (Denmark)

    Alanne, Tommi; Franzosi, Diogo Buarque; Frandsen, Mads T.

    2017-01-01

    We consider a model of dynamical electroweak symmetry breaking with a partially composite Goldstone Higgs boson. The model is based on a strongly interacting fermionic sector coupled to a fundamental scalar sector via Yukawa interactions. The SU(4)×SU(4) global symmetry of these two sectors...... is broken to a single SU(4) via Yukawa interactions. Electroweak symmetry breaking is dynamically induced by condensation due to the strong interactions in the new fermionic sector which further breaks the global symmetry SU(4)→Sp(4). The Higgs boson arises as a partially composite state which is an exact...... Goldstone boson in the limit where SM interactions are turned off. Terms breaking the SU(4) global symmetry explicitly generate a mass for the Goldstone Higgs boson. The model realizes in different limits both (partially) composite Higgs and (bosonic) technicolor models, thereby providing a convenient...

  16. Control of stochastic resonance in bistable systems by using periodic signals

    International Nuclear Information System (INIS)

    Min, Lin; Li-Min, Fang; Yong-Jun, Zheng

    2009-01-01

    According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal. Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization. By adding a bistable system with a controllable periodic signal, fluctuations in the single potential well can be effectively controlled, thus affecting the probability transitions between the two potential wells. In this way, an effective control can be achieved which allows one to either enhance or realize stochastic resonance

  17. Some Considerations on the Partial Credit Model

    OpenAIRE

    H.H.F.M. Verstralen; N.D. Verhelst

    2008-01-01

    The Partial Credit Model (PCM) is sometimes interpreted as a model for stepwise solution of polytomously scored items, where the item parameters are interpreted as di culties of the steps. It is argued that this interpretation is not justi ed. A model for stepwise solution is discussed. It is shown that the PCM is suited to model sums of binary responses which are not supposed to be stochastically independent. As a practical result, a statistical test of sto...

  18. Partial Safety Factors and Target Reliability Level in Danish Structural Codes

    DEFF Research Database (Denmark)

    Sørensen, John Dalsgaard; Hansen, J. O.; Nielsen, T. A.

    2001-01-01

    The partial safety factors in the newly revised Danish structural codes have been derived using a reliability-based calibration. The calibrated partial safety factors result in the same average reliability level as in the previous codes, but a much more uniform reliability level has been obtained....... The paper describes the code format, the stochastic models and the resulting optimised partial safety factors....

  19. Simulation of the stochastic wave loads using a physical modeling approach

    DEFF Research Database (Denmark)

    Liu, W.F.; Sichani, Mahdi Teimouri; Nielsen, Søren R.K.

    2013-01-01

    In analyzing stochastic dynamic systems, analysis of the system uncertainty due to randomness in the loads plays a crucial role. Typically time series of the stochastic loads are simulated using traditional random phase method. This approach combined with fast Fourier transform algorithm makes...... reliability or its uncertainty. Moreover applicability of the probability density evolution method on engineering problems faces critical difficulties when the system embeds too many random variables. Hence it is useful to devise a method which can make realization of the stochastic load processes with low...

  20. Distributed parallel computing in stochastic modeling of groundwater systems.

    Science.gov (United States)

    Dong, Yanhui; Li, Guomin; Xu, Haizhen

    2013-03-01

    Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

  1. Stochastic models of the Social Security trust funds.

    Science.gov (United States)

    Burdick, Clark; Manchester, Joyce

    Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.

  2. A retrodictive stochastic simulation algorithm

    International Nuclear Information System (INIS)

    Vaughan, T.G.; Drummond, P.D.; Drummond, A.J.

    2010-01-01

    In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.

  3. Stochastic processes and quantum theory

    International Nuclear Information System (INIS)

    Klauder, J.R.

    1975-01-01

    The author analyses a variety of stochastic processes, namely real time diffusion phenomena, which are analogues of imaginary time quantum theory and convariant imaginary time quantum field theory. He elaborates some standard properties involving probability measures and stochastic variables and considers a simple class of examples. Finally he develops the fact that certain stochastic theories actually exhibit divergences that simulate those of covariant quantum field theory and presents examples of both renormaizable and unrenormalizable behavior. (V.J.C.)

  4. A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion

    Directory of Open Access Journals (Sweden)

    O. H. Galal

    2013-01-01

    Full Text Available This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC. The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE into a set of coupled deterministic partial differential equations and then solved using finite difference method. Two well-known equations were used for efficiency validation of the method proposed. First one being the linear diffusion equation with stochastic parameter and the second is the nonlinear Burger's equation with stochastic parameter and stochastic initial and boundary conditions. In both of these examples, the probability distribution function of the response manifested close conformity to the results obtained from Monte Carlo simulation with optimized computational cost.

  5. Stochastic heat and Burgers equations and their singularities II - Analytical Properties and Limiting Distributions

    CERN Document Server

    Davies, I M; Zhao, H

    2004-01-01

    We study the inviscid limit, $\\mu\\to 0$, of the stochastic viscous Burgers equation, for the velocity field $v^{\\mu}(x,t)$, $t>0$, $x\\in\\mathbb R^d$,\\frac{\\partial{v^{\\mu}}}{\\partial{t}} + (v^{\\mu}\\cdot\

  6. Superworld volume dynamics of super branes from nonlinear realizations

    International Nuclear Information System (INIS)

    Bellucci, S.; Ivanov, E.; Krivonos, S.

    2000-01-01

    Based on the concept of the partial breaking of global supersymmetry (PBGS), it has been derived the world volume superfield equations of motion for N=1, D=4 supermembrane, as well as for the space-time filling D2- and D3-branes, from nonlinear realizations of the corresponding supersymmetries. It has been argued that it is of no need to take care of the relevant automorphism groups when being interested in the dynamical equations. This essentially facilitates computations. As a by-product, it has been obtained a new polynomial representation for the d=3,4 Born-Infeld equations, with merely a cubic nonlinearity

  7. Stochastic Analysis with Financial Applications

    CERN Document Server

    Kohatsu-Higa, Arturo; Sheu, Shuenn-Jyi

    2011-01-01

    Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. This book also covers the areas of backward stochastic differential equations via the (non-li

  8. Large deviations for solutions to stochastic recurrence equations under Kesten's condition

    DEFF Research Database (Denmark)

    Buraczewski, Dariusz; Damek, Ewa; Mikosch, Thomas Valentin

    2013-01-01

    In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten’s condition [17] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise...... sequence of the equations can have light tails. The results of the paper are analogs of those obtained by A.V. and S.V. Nagaev [21, 22] in the case of partial sums of iid random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest...... step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies...

  9. Modelling and Forecasting Multivariate Realized Volatility

    DEFF Research Database (Denmark)

    Chiriac, Roxana; Voev, Valeri

    . We provide an empirical application of the model, in which we show by means of stochastic dominance tests that the returns from an optimal portfolio based on the model's forecasts second-order dominate returns of portfolios optimized on the basis of traditional MGARCH models. This result implies...

  10. The stochastic spectator

    Energy Technology Data Exchange (ETDEWEB)

    Hardwick, Robert J.; Vennin, Vincent; Wands, David [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom); Byrnes, Christian T.; Torrado, Jesús, E-mail: robert.hardwick@port.ac.uk, E-mail: vincent.vennin@port.ac.uk, E-mail: c.byrnes@sussex.ac.uk, E-mail: jesus.torrado@sussex.ac.uk, E-mail: david.wands@port.ac.uk [Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH (United Kingdom)

    2017-10-01

    We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.

  11. The stochastic spectator

    International Nuclear Information System (INIS)

    Hardwick, Robert J.; Vennin, Vincent; Wands, David; Byrnes, Christian T.; Torrado, Jesús

    2017-01-01

    We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.

  12. Microgrid Reliability Modeling and Battery Scheduling Using Stochastic Linear Programming

    Energy Technology Data Exchange (ETDEWEB)

    Cardoso, Goncalo; Stadler, Michael; Siddiqui, Afzal; Marnay, Chris; DeForest, Nicholas; Barbosa-Povoa, Ana; Ferrao, Paulo

    2013-05-23

    This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6percent.

  13. Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

    Science.gov (United States)

    Varga, Katherine Yvonne

    2015-01-01

    We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

  14. Stochastic ontogenetic growth model

    Science.gov (United States)

    West, B. J.; West, D.

    2012-02-01

    An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.

  15. Stochastic calculus in physics

    International Nuclear Information System (INIS)

    Fox, R.F.

    1987-01-01

    The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations

  16. The stochastic quality calculus

    DEFF Research Database (Denmark)

    Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis

    2014-01-01

    We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...... with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...

  17. Stochastic conditional intensity processes

    DEFF Research Database (Denmark)

    Bauwens, Luc; Hautsch, Nikolaus

    2006-01-01

    model allows for a wide range of (cross-)autocorrelation structures in multivariate point processes. The model is estimated by simulated maximum likelihood (SML) using the efficient importance sampling (EIS) technique. By modeling price intensities based on NYSE trading, we provide significant evidence......In this article, we introduce the so-called stochastic conditional intensity (SCI) model by extending Russell’s (1999) autoregressive conditional intensity (ACI) model by a latent common dynamic factor that jointly drives the individual intensity components. We show by simulations that the proposed...... for a joint latent factor and show that its inclusion allows for an improved and more parsimonious specification of the multivariate intensity process...

  18. Stochastic cooling for beginners

    International Nuclear Information System (INIS)

    Moehl, D.

    1984-01-01

    These two lectures have been prepared to give a simple introduction to the principles. In Part I we try to explain stochastic cooling using the time-domain picture which starts from the pulse response of the system. In Part II the discussion is repeated, looking more closely at the frequency-domain response. An attempt is made to familiarize the beginners with some of the elementary cooling equations, from the 'single particle case' up to equations which describe the evolution of the particle distribution. (orig.)

  19. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-01-01

    to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

  20. Stochastic Blind Motion Deblurring

    KAUST Repository

    Xiao, Lei

    2015-05-13

    Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.

  1. Simple stochastic simulation.

    Science.gov (United States)

    Schilstra, Maria J; Martin, Stephen R

    2009-01-01

    Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.

  2. AA, stochastic precooling pickup

    CERN Multimedia

    CERN PhotoLab

    1980-01-01

    The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...

  3. Behavioral Stochastic Resonance

    Science.gov (United States)

    Freund, Jan A.; Schimansky-Geier, Lutz; Beisner, Beatrix; Neiman, Alexander; Russell, David F.; Yakusheva, Tatyana; Moss, Frank

    2001-03-01

    Zooplankton emit weak electric fields into the surrounding water that originate from their own muscular activities associated with swimming and feeding. Juvenile paddlefish prey upon single zooplankton by detecting and tracking these weak electric signatures. The passive electric sense in the fish is provided by an elaborate array of electroreceptors, Ampullae Lorenzini, spread over the surface of an elongated rostrum. We have previously shown that the fish use stochastic resonance to enhance prey capture near the detection threshold of their sensory system. But stochastic resonance requires an external source of electrical noise in order to function. The required noise can be provided by a swarm of plankton, for example Daphnia. Thus juvenile paddlefish can detect and attack single Daphnia as outliers in the vicinity of the swarm by making use of noise from the swarm itself. From the power spectral density of the noise plus the weak signal from a single Daphnia we calculate the signal-to-noise ratio and the Fisher information at the surface of the paddlefish's rostrum. The results predict a specific attack pattern for the paddlefish that appears to be experimentally testable.

  4. Stochastic programming with integer recourse

    NARCIS (Netherlands)

    van der Vlerk, Maarten Hendrikus

    1995-01-01

    In this thesis we consider two-stage stochastic linear programming models with integer recourse. Such models are at the intersection of two different branches of mathematical programming. On the one hand some of the model parameters are random, which places the problem in the field of stochastic

  5. Thermal mixtures in stochastic mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Guerra, F [Rome Univ. (Italy). Ist. di Matematica; Loffredo, M I [Salerno Univ. (Italy). Ist. di Fisica

    1981-01-17

    Stochastic mechanics is extended to systems in thermal equilibrium. The resulting stochastic processes are mixtures of Nelson processes. Their Markov property is investigated in some simple cases. It is found that in order to inforce Markov property the algebra of observable associated to the present must be suitably enlarged.

  6. Stochastic Pi-calculus Revisited

    DEFF Research Database (Denmark)

    Cardelli, Luca; Mardare, Radu Iulian

    2013-01-01

    We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

  7. Alternative Asymmetric Stochastic Volatility Models

    NARCIS (Netherlands)

    M. Asai (Manabu); M.J. McAleer (Michael)

    2010-01-01

    textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is

  8. Stochastic ferromagnetism analysis and numerics

    CERN Document Server

    Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas

    2013-01-01

    This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.

  9. Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity

    KAUST Repository

    Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

    2016-01-01

    We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM

  10. Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity

    KAUST Repository

    Haji Ali, Abdul Lateef

    2016-08-26

    We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM

  11. Sampling from stochastic reservoir models constrained by production data

    Energy Technology Data Exchange (ETDEWEB)

    Hegstad, Bjoern Kaare

    1997-12-31

    When a petroleum reservoir is evaluated, it is important to forecast future production of oil and gas and to assess forecast uncertainty. This is done by defining a stochastic model for the reservoir characteristics, generating realizations from this model and applying a fluid flow simulator to the realizations. The reservoir characteristics define the geometry of the reservoir, initial saturation, petrophysical properties etc. This thesis discusses how to generate realizations constrained by production data, that is to say, the realizations should reproduce the observed production history of the petroleum reservoir within the uncertainty of these data. The topics discussed are: (1) Theoretical framework, (2) History matching, forecasting and forecasting uncertainty, (3) A three-dimensional test case, (4) Modelling transmissibility multipliers by Markov random fields, (5) Up scaling, (6) The link between model parameters, well observations and production history in a simple test case, (7) Sampling the posterior using optimization in a hierarchical model, (8) A comparison of Rejection Sampling and Metropolis-Hastings algorithm, (9) Stochastic simulation and conditioning by annealing in reservoir description, and (10) Uncertainty assessment in history matching and forecasting. 139 refs., 85 figs., 1 tab.

  12. Brownian motion and stochastic calculus

    CERN Document Server

    Karatzas, Ioannis

    1998-01-01

    This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

  13. Supertrace formulae for nonlinearly realized supersymmetry

    Science.gov (United States)

    Murli, Divyanshu; Yamada, Yusuke

    2018-04-01

    We derive the general supertrace formula for a system with N chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral superfield breaking supersymmetry spontaneously. As we show, however, the modified formula is not simply related to the scalar-decoupling limit of the supertrace in linearly-realized supersymmetry. We also show that the supertrace formula reduces to that of a linearly realized supersymmetric theory with a decoupled sGoldstino if the Goldstino is the fermion in the nilpotent multiplet.

  14. SELANSI: a toolbox for simulation of stochastic gene regulatory networks.

    Science.gov (United States)

    Pájaro, Manuel; Otero-Muras, Irene; Vázquez, Carlos; Alonso, Antonio A

    2018-03-01

    Gene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort. This work presents SELANSI (SEmi-LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi-lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options. SELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi. antonio@iim.csic.es. © The Author(s) 2017. Published by Oxford University Press.

  15. Product Realization | College of Engineering & Applied Science

    Science.gov (United States)

    Olympiad Girls Who Code Club FIRST Tech Challenge NSF I-Corps Site of Southeastern Wisconsin UW-Milwaukee Product Realization Course Companies need time and talent to develop new product prototypes. Students need

  16. Modelling and Forecasting Multivariate Realized Volatility

    DEFF Research Database (Denmark)

    Halbleib, Roxana; Voev, Valeri

    2011-01-01

    This paper proposes a methodology for dynamic modelling and forecasting of realized covariance matrices based on fractionally integrated processes. The approach allows for flexible dependence patterns and automatically guarantees positive definiteness of the forecast. We provide an empirical appl...

  17. Researchers Realize Major Breakthrough in Understanding Endometriosis

    Science.gov (United States)

    ... 16, 2014 Researchers Realize Major Breakthrough in Understanding Endometriosis For a disease that affects an estimated 6 ... 10% of women, surprisingly little is known about endometriosis — a disorder that causes uterine tissue to grow ...

  18. Infinite Dimensional Stochastic Analysis : in Honor of Hui-Hsiung Kuo

    CERN Document Server

    Sundar, Pushpa

    2008-01-01

    This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate

  19. A Stochastic Delay Model For Pricing Debt And Loan Guarantees: Theoretical Results

    OpenAIRE

    Kemajou, Elisabeth; Mohammed, Salah-Eldin; Tambue, Antoine

    2012-01-01

    We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partial Differential Equation (RPDE) satisfied by any corporate claim whose value is a function of firm value and time. Under specific final and boundary conditions, we solve the RPDE...

  20. psychrometry: from partial pressures to mole fractions

    African Journals Online (AJOL)

    ES Obe

    1980-03-01

    Mar 1, 1980 ... as an ideal gas mixture. Partial pressures then become identical: to mole fractions and sets of psychometric parameters result from rather elementary thermodynamic relations. Search for more accurate data has long led to the realization that neither dry air nor pure water vapour behaves like an ideal gas,.

  1. Nonlinear realizations of W3 symmetry

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Krivonos, S.O.

    1991-01-01

    We derive the Toda lattice realization of classical W 3 symmetry on two scalar fields in a purely geometric way, proceeding from a nonlinear realization of some associate higher-spin symmetry W 3 ∞ is derived. The Toda lattice equations are interpreted as the constraints singling out a two-dimensional fully geodesic subspace in the initial coset space of W 3 ∞ . This subspace is the quotient of SL(3,R) over its maximal parabolic subgroup. 20 refs

  2. Learning, Realizability and Games in Classical Arithmetic

    Science.gov (United States)

    Aschieri, Federico

    2010-12-01

    In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully detailed constructive analysis of learning as it arises in learning based realizability for HA+EM1, Avigad's update procedures and epsilon substitution method for Peano Arithmetic PA. We present new constructive techniques to bound the length of learning processes and we apply them to reprove - by means of our theory - the classic result of Godel that provably total functions of PA can be represented in Godel's system T. Last, we give an axiomatization of the kind of learning that is needed to computationally interpret Predicative classical second order Arithmetic. Our work is an extension of Avigad's and generalizes the concept of update procedure to the transfinite case. Transfinite update procedures have to learn values of transfinite sequences of non computable functions in order to extract witnesses from classical proofs.

  3. Realization of FRC interior and exterior furniture

    Science.gov (United States)

    Šonka, Š.; Frantová, M.; Štemberk, P.; Havrda, J.; Janouch, P.

    2017-09-01

    This article deals with the implementation of fibre reinforced concrete for interior and exterior furniture. The use of fibre reinforced concrete for non-traditional and small structures brings some specifics in design and realization. These are, in particular, the design of a suitable mixture, the choice of the shape of the structure in relation to the technological possibilities of realization, the static effects and finally the actual production of the element.

  4. The linguistic realization of information packaging

    OpenAIRE

    Vallduví, Enric; Engdahl, Elisabet

    1996-01-01

    There is increasing awareness of the large degree of crosslinguistic diversity involved in the structural realization of information packaging (or information structure). Whereas English and many Germanic languages primarily exploit intonation for informational purposes, in other languages, like Catalan, syntax plays the primary role in the realization of information packaging and intonation is reduced to a secondary role. In yet another group of languages the primary structural correlate is ...

  5. Applied stochastic modelling

    CERN Document Server

    Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P

    2008-01-01

    Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...

  6. Stochastic population theories

    CERN Document Server

    Ludwig, Donald

    1974-01-01

    These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the Na...

  7. Propagator of stochastic electrodynamics

    International Nuclear Information System (INIS)

    Cavalleri, G.

    1981-01-01

    The ''elementary propagator'' for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density proportionalω 3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to psipsi* where psi is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics

  8. Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Hong [Pacific Northwest National Laboratory (PNNL); Aziz, H M Abdul [ORNL; Young, Stan [National Renewable Energy Laboratory (NREL); Patil, Sagar [Pacific Northwest National Laboratory (PNNL)

    2017-10-01

    Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections. In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.

  9. Hybrid stochastic simplifications for multiscale gene networks

    Directory of Open Access Journals (Sweden)

    Debussche Arnaud

    2009-09-01

    Full Text Available Abstract Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion 123 which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.

  10. Models for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices

    DEFF Research Database (Denmark)

    Christoffersen, Peter; Jacobs, Kris; Mimouni, Karim

    in the search for alternative specifications. We then estimate the models using maximum likelihood on S&P500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data......Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases. We investigate...... alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us...

  11. Stochastic estimation of electricity consumption

    International Nuclear Information System (INIS)

    Kapetanovic, I.; Konjic, T.; Zahirovic, Z.

    1999-01-01

    Electricity consumption forecasting represents a part of the stable functioning of the power system. It is very important because of rationality and increase of control process efficiency and development planning of all aspects of society. On a scientific basis, forecasting is a possible way to solve problems. Among different models that have been used in the area of forecasting, the stochastic aspect of forecasting as a part of quantitative models takes a very important place in applications. ARIMA models and Kalman filter as stochastic estimators have been treated together for electricity consumption forecasting. Therefore, the main aim of this paper is to present the stochastic forecasting aspect using short time series. (author)

  12. Linear stochastic neutron transport theory

    International Nuclear Information System (INIS)

    Lewins, J.

    1978-01-01

    A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)

  13. Stochasticity in the Josephson map

    International Nuclear Information System (INIS)

    Nomura, Y.; Ichikawa, Y.H.; Filippov, A.T.

    1996-04-01

    The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)

  14. Introduction to stochastic dynamic programming

    CERN Document Server

    Ross, Sheldon M; Lukacs, E

    1983-01-01

    Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the

  15. On-off intermittency and coherent bursting in stochastically-driven coupled maps

    International Nuclear Information System (INIS)

    Metta, Sabino; Provenzale, Antonello; Spiegel, Edward A.

    2010-01-01

    On-off intermittency is a phase space mechanism for bursting in dynamical systems. Here we recall how the simple example of a logistic map with a time-dependent control parameter, considered as a dynamical variable of the system, gives rise to bursting or on-off behavior. We show that, for a given realization of the driver, a stochastically driven logistic map in the on-off intermittent regime always converges to the same temporal dynamics, independently of initial conditions. In that sense, the map is not chaotic. We then explore the behavior of two coupled on-off logistic maps, each driven by a separate random process, and show that, for a wide range of coupling strengths, bursting becomes at least partially coherent. The bursting coherence has a smooth dependence on the coupling parameter and no sharp transition from coherence to incoherence is detected. In the system of two coupled on-off maps studied here, coherent bursting is rooted in the behavior during off phases when the mapped coordinates take on extremely small values.

  16. Quantum simulation of a quantum stochastic walk

    Science.gov (United States)

    Govia, Luke C. G.; Taketani, Bruno G.; Schuhmacher, Peter K.; Wilhelm, Frank K.

    2017-03-01

    The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk (QSW), which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a QSW can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of QSWs that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of QSWs, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of QSWs on large graphs with existing quantum technologies.

  17. Functional Abstraction of Stochastic Hybrid Systems

    NARCIS (Netherlands)

    Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.

    2006-01-01

    The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways

  18. An introduction to probability and stochastic processes

    CERN Document Server

    Melsa, James L

    2013-01-01

    Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

  19. Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller

    Directory of Open Access Journals (Sweden)

    Zengyun Wang

    2013-01-01

    Full Text Available This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

  20. Approximation of itô integrals arising in stochastic time-delayed systems

    NARCIS (Netherlands)

    Bagchi, Arunabha

    1984-01-01

    Likelihood functional for stochastic linear time-delayed systems involve Itô integrals with respect to the observed data. Since the Wiener process appearing in the standard observation process model for such systems is not realizable and the physically observed process is smooth, one needs to study

  1. Elements of stochastic calculus and analysis

    CERN Document Server

    Stroock, Daniel W

    2018-01-01

    This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered here has appeared in other places, this book attempts to explain the core ideas on which that material is based. As a consequence, the presentation is more an extended mathematical essay than a ``definition, lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example, Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application of Malliavin's calculus to partial differential equations. Each chapter concludes with several exercises, some of which are quite challenging. The book is intended for use by advanced graduate students and research mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.

  2. Stochastic backgrounds of gravitational waves

    International Nuclear Information System (INIS)

    Maggiore, M.

    2001-01-01

    We review the motivations for the search for stochastic backgrounds of gravitational waves and we compare the experimental sensitivities that can be reached in the near future with the existing bounds and with the theoretical predictions. (author)

  3. Stochastic theories of quantum mechanics

    International Nuclear Information System (INIS)

    De la Pena, L.; Cetto, A.M.

    1991-01-01

    The material of this article is organized into five sections. In Sect. I the basic characteristics of quantum systems are briefly discussed, with emphasis on their stochastic properties. In Sect. II a version of stochastic quantum mechanics is presented, to conclude that the quantum formalism admits an interpretation in terms of stochastic processes. In Sect. III the elements of stochastic electrodynamics are described, and its possibilities and limitations as a fundamental theory of quantum systems are discussed. Section IV contains a recent reformulation that overcomes the limitations of the theory discussed in the foregoing section. Finally, in Sect. V the theorems of EPR, Von Neumann and Bell are discussed briefly. The material is pedagogically presented and includes an ample list of references, but the details of the derivations are generally omitted. (Author)

  4. A stochastic picture of spin

    International Nuclear Information System (INIS)

    Faris, W.G.

    1981-01-01

    Dankel has shown how to incorporate spin into stochastic mechanics. The resulting non-local hidden variable theory gives an appealing picture of spin correlation experiments in which Bell's inequality is violated. (orig.)

  5. Statistical inference for stochastic processes

    National Research Council Canada - National Science Library

    Basawa, Ishwar V; Prakasa Rao, B. L. S

    1980-01-01

    The aim of this monograph is to attempt to reduce the gap between theory and applications in the area of stochastic modelling, by directing the interest of future researchers to the inference aspects...

  6. Stochastic singular optics (Conference paper)

    CSIR Research Space (South Africa)

    Roux, FS

    2014-09-01

    Full Text Available The study of optical vortices in stochastic optical fields involves various quantities, including the vortex density and topological charge density, that are defined in terms of local expectation values of distributions of optical vortices...

  7. Stochastic equations theory and applications in acoustics, hydrodynamics, magnetohydrodynamics, and radiophysics

    CERN Document Server

    Klyatskin, Valery I

    2015-01-01

    This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.  

  8. Aperiodic signals processing via parameter-tuning stochastic resonance in a photorefractive ring cavity

    Directory of Open Access Journals (Sweden)

    Xuefeng Li

    2014-04-01

    Full Text Available Based on solving numerically the generalized nonlinear Langevin equation describing the nonlinear dynamics of stochastic resonance by Fourth-order Runge-Kutta method, an aperiodic stochastic resonance based on an optical bistable system is numerically investigated. The numerical results show that a parameter-tuning stochastic resonance system can be realized by choosing the appropriate optical bistable parameters, which performs well in reconstructing aperiodic signals from a very high level of noise background. The influences of optical bistable parameters on the stochastic resonance effect are numerically analyzed via cross-correlation, and a maximum cross-correlation gain of 8 is obtained by optimizing optical bistable parameters. This provides a prospective method for reconstructing noise-hidden weak signals in all-optical signal processing systems.

  9. Stochastic massless fields I: Integer spin

    International Nuclear Information System (INIS)

    Lim, S.C.

    1981-04-01

    Nelson's stochastic quantization scheme is applied to classical massless tensor potential in ''Coulomb'' gauge. The relationship between stochastic potential field in various gauges is discussed using the case of vector potential as an illustration. It is possible to identify the Euclidean tensor potential with the corresponding stochastic field in physical Minkowski space-time. Stochastic quantization of massless fields can also be carried out in terms of field strength tensors. An example of linearized stochastic gravitational field in vacuum is given. (author)

  10. Stochastic theory of fatigue corrosion

    Science.gov (United States)

    Hu, Haiyun

    1999-10-01

    A stochastic theory of corrosion has been constructed. The stochastic equations are described giving the transportation corrosion rate and fluctuation corrosion coefficient. In addition the pit diameter distribution function, the average pit diameter and the most probable pit diameter including other related empirical formula have been derived. In order to clarify the effect of stress range on the initiation and growth behaviour of pitting corrosion, round smooth specimen were tested under cyclic loading in 3.5% NaCl solution.

  11. Stochastic quantization and gauge theories

    International Nuclear Information System (INIS)

    Kolck, U. van.

    1987-01-01

    Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author) [pt

  12. Stochasticity induced by coherent wavepackets

    International Nuclear Information System (INIS)

    Fuchs, V.; Krapchev, V.; Ram, A.; Bers, A.

    1983-02-01

    We consider the momentum transfer and diffusion of electrons periodically interacting with a coherent longitudinal wavepacket. Such a problem arises, for example, in lower-hybrid current drive. We establish the stochastic threshold, the stochastic region δv/sub stoch/ in velocity space, the associated momentum transfer j, and the diffusion coefficient D. We concentrate principally on the weak-field regime, tau/sub autocorrelation/ < tau/sub bounce/

  13. Stochastic runaway of dynamical systems

    International Nuclear Information System (INIS)

    Pfirsch, D.; Graeff, P.

    1984-10-01

    One-dimensional, stochastic, dynamical systems are well studied with respect to their stability properties. Less is known for the higher dimensional case. This paper derives sufficient and necessary criteria for the asymptotic divergence of the entropy (runaway) and sufficient ones for the moments of n-dimensional, stochastic, dynamical systems. The crucial implication is the incompressibility of their flow defined by the equations of motion in configuration space. Two possible extensions to compressible flow systems are outlined. (orig.)

  14. Stochastic Models of Polymer Systems

    Science.gov (United States)

    2016-01-01

    Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...ADDRESS. Princeton University PO Box 0036 87 Prospect Avenue - 2nd floor Princeton, NJ 08544 -2020 14-Mar-2014 ABSTRACT Number of Papers published in...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title

  15. Stochastic efficiency: five case studies

    International Nuclear Information System (INIS)

    Proesmans, Karel; Broeck, Christian Van den

    2015-01-01

    Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic efficiency, including the maximum of the large deviation function at the reversible efficiency, are reproduced. The approach to and extrapolation into the asymptotic time regime are documented. (paper)

  16. Optimal Liquidation under Stochastic Liquidity

    OpenAIRE

    Becherer, Dirk; Bilarev, Todor; Frentrup, Peter

    2016-01-01

    We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the inter-temporal resilience of the market in spirit of Predoiu, Shaikhet and Shreve (2011), is taken to be stochastic, being driven by own random noise. The optimal contro...

  17. Memory effects on stochastic resonance

    Science.gov (United States)

    Neiman, Alexander; Sung, Wokyung

    1996-02-01

    We study the phenomenon of stochastic resonance (SR) in a bistable system with internal colored noise. In this situation the system possesses time-dependent memory friction connected with noise via the fluctuation-dissipation theorem, so that in the absence of periodic driving the system approaches the thermodynamic equilibrium state. For this non-Markovian case we find that memory usually suppresses stochastic resonance. However, for a large memory time SR can be enhanced by the memory.

  18. Stochastic optimization: beyond mathematical programming

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Stochastic optimization, among which bio-inspired algorithms, is gaining momentum in areas where more classical optimization algorithms fail to deliver satisfactory results, or simply cannot be directly applied. This presentation will introduce baseline stochastic optimization algorithms, and illustrate their efficiency in different domains, from continuous non-convex problems to combinatorial optimization problem, to problems for which a non-parametric formulation can help exploring unforeseen possible solution spaces.

  19. Stochastic quantization and gauge invariance

    International Nuclear Information System (INIS)

    Viana, R.L.

    1987-01-01

    A survey of the fundamental ideas about Parisi-Wu's Stochastic Quantization Method, with applications to Scalar, Gauge and Fermionic theories, is done. In particular, the Analytic Stochastic Regularization Scheme is used to calculate the polarization tensor for Quantum Electrodynamics with Dirac bosons or Fermions. The regularization influence is studied for both theories and an extension of this method for some supersymmetrical models is suggested. (author)

  20. Stochastic Analysis and Related Topics

    CERN Document Server

    Ustunel, Ali

    1988-01-01

    The Silvri Workshop was divided into a short summer school and a working conference, producing lectures and research papers on recent developments in stochastic analysis on Wiener space. The topics treated in the lectures relate to the Malliavin calculus, the Skorohod integral and nonlinear functionals of white noise. Most of the research papers are applications of these subjects. This volume addresses researchers and graduate students in stochastic processes and theoretical physics.

  1. Synthetic Computation: Chaos Computing, Logical Stochastic Resonance, and Adaptive Computing

    Science.gov (United States)

    Kia, Behnam; Murali, K.; Jahed Motlagh, Mohammad-Reza; Sinha, Sudeshna; Ditto, William L.

    Nonlinearity and chaos can illustrate numerous behaviors and patterns, and one can select different patterns from this rich library of patterns. In this paper we focus on synthetic computing, a field that engineers and synthesizes nonlinear systems to obtain computation. We explain the importance of nonlinearity, and describe how nonlinear systems can be engineered to perform computation. More specifically, we provide an overview of chaos computing, a field that manually programs chaotic systems to build different types of digital functions. Also we briefly describe logical stochastic resonance (LSR), and then extend the approach of LSR to realize combinational digital logic systems via suitable concatenation of existing logical stochastic resonance blocks. Finally we demonstrate how a chaotic system can be engineered and mated with different machine learning techniques, such as artificial neural networks, random searching, and genetic algorithm, to design different autonomous systems that can adapt and respond to environmental conditions.

  2. Inverse Higgs effect in nonlinear realizations

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Ogievetskij, V.I.

    1975-01-01

    In theories with nonlinearly realized symmetry it is possible in a number of cases to eliminate some initial Goldstone and gauge fields by means of putting appropriate Cartan forms equal to zero. This is called the inverse Higgs phenomenon. We give a general treatment of the inverse Higgs phenomenon for gauge and space-time symmetries and consider four instructive examples which are the elimination of unessential gauge fields in chiral symmetry and in non-linearly realized supersymmetry and also the elimination of unessential Goldstone fields in the spontaneously broken conformal and projective symmetries

  3. Phenomenology of stochastic exponential growth

    Science.gov (United States)

    Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

    2017-06-01

    Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

  4. On square-wave-driven stochastic resonance for energy harvesting in a bistable system

    Energy Technology Data Exchange (ETDEWEB)

    Su, Dongxu, E-mail: sudx@iis.u-tokyo.ac.jp [Graduate School of Engineering, The University of Tokyo, Tokyo 1538505 (Japan); Zheng, Rencheng; Nakano, Kimihiko [Institute of Industrial Science, The University of Tokyo, Tokyo 1538505 (Japan); Cartmell, Matthew P [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)

    2014-11-15

    Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation.

  5. On square-wave-driven stochastic resonance for energy harvesting in a bistable system

    International Nuclear Information System (INIS)

    Su, Dongxu; Zheng, Rencheng; Nakano, Kimihiko; Cartmell, Matthew P

    2014-01-01

    Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation

  6. Stochastic Effects in Microstructure

    Directory of Open Access Journals (Sweden)

    Glicksman M.E.

    2002-01-01

    Full Text Available We are currently studying microstructural responses to diffusion-limited coarsening in two-phase materials. A mathematical solution to late-stage multiparticle diffusion in finite systems is formulated with account taken of particle-particle interactions and their microstructural correlations, or "locales". The transition from finite system behavior to that for an infinite microstructure is established analytically. Large-scale simulations of late-stage phase coarsening dynamics show increased fluctuations with increasing volume fraction, Vv, of the mean flux entering or leaving particles of a given size class. Fluctuations about the mean flux were found to depend on the scaled particle size, R/, where R is the radius of a particle and is the radius of the dispersoid averaged over the population within the microstructure. Specifically, small (shrinking particles tend to display weak fluctuations about their mean flux, whereas particles of average, or above average size, exhibit strong fluctuations. Remarkably, even in cases of microstructures with a relatively small volume fraction (Vv ~ 10-4, the particle size distribution is broader than that for the well-known Lifshitz-Slyozov limit predicted at zero volume fraction. The simulation results reported here provide some additional surprising insights into the effect of diffusion interactions and stochastic effects during evolution of a microstructure, as it approaches its thermodynamic end-state.

  7. Adaptation in stochastic environments

    CERN Document Server

    Clark, Colib

    1993-01-01

    The classical theory of natural selection, as developed by Fisher, Haldane, and 'Wright, and their followers, is in a sense a statistical theory. By and large the classical theory assumes that the underlying environment in which evolution transpires is both constant and stable - the theory is in this sense deterministic. In reality, on the other hand, nature is almost always changing and unstable. We do not yet possess a complete theory of natural selection in stochastic environ­ ments. Perhaps it has been thought that such a theory is unimportant, or that it would be too difficult. Our own view is that the time is now ripe for the development of a probabilistic theory of natural selection. The present volume is an attempt to provide an elementary introduction to this probabilistic theory. Each author was asked to con­ tribute a simple, basic introduction to his or her specialty, including lively discussions and speculation. We hope that the book contributes further to the understanding of the roles of "Cha...

  8. Stochastic Methods in Biology

    CERN Document Server

    Kallianpur, Gopinath; Hida, Takeyuki

    1987-01-01

    The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis­ cipline with its own repertoire of techniques. The purpose of the Workshop on sto­ chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap­ plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important f...

  9. AA, stochastic precooling kicker

    CERN Multimedia

    CERN PhotoLab

    1980-01-01

    The freshly injected antiprotons were subjected to fast stochastic "precooling", while a shutter shielded the deeply cooled antiproton stack from the violent action of the precooling kicker. In this picture, the injection orbit is to the left, the stack orbit to the far right, the separating shutter is in open position. After several seconds of precooling (in momentum and in the vertical plane), the shutter was opened briefly, so that by means of RF the precooled antiprotons could be transferred to the stack tail, where they were subjected to further cooling in momentum and both transverse planes, until they ended up, deeply cooled, in the stack core. The fast shutter, which had to open and close in a fraction of a second was an essential item of the cooling scheme and a mechanical masterpiece. Here the shutter is in the open position. The precooling pickups were of the same design, with the difference that the kickers had cooling circuits and the pickups not. 8401150 shows a precooling pickup with the shutte...

  10. Non-linear realizations and bosonic branes

    International Nuclear Information System (INIS)

    West, P.

    2001-01-01

    In this very short note, following hep-th/0001216, we express the well known bosonic brane as a non-linear realization. The reader may also consult hep-th/9912226, 0001216 and 0005270 where the branes of M theory are constructed as a non-linear realisation. The automorphisms of the supersymmetry algebra play an essential role. (author)

  11. Nonlinear realization of general covariance group

    International Nuclear Information System (INIS)

    Hamamoto, Shinji

    1979-01-01

    The structure of the theory resulting from the nonlinear realization of general covariance group is analysed. We discuss the general form of free Lagrangian for Goldstone fields, and propose as a special choice one reasonable form which is shown to describe a gravitational theory with massless tensor graviton and massive vector tordion. (author)

  12. The economic value of realized volatility

    DEFF Research Database (Denmark)

    Christoffersen, Peter; Feunou, Bruno; Jacobs, Kris

    2014-01-01

    Many studies have documented that daily realized volatility estimates based on intraday returns provide volatility forecasts that are superior to forecasts constructed from daily returns only. We investigate whether these forecasting improvements translate into economic value added. To do so, we ...

  13. Banach spaces that realize minimal fillings

    International Nuclear Information System (INIS)

    Bednov, B. B.; Borodin, P. A.

    2014-01-01

    It is proved that a real Banach space realizes minimal fillings for all its finite subsets (a shortest network spanning a fixed finite subset always exists and has the minimum possible length) if and only if it is a predual of L 1 . The spaces L 1 are characterized in terms of Steiner points (medians). Bibliography: 25 titles. (paper)

  14. Zero-intelligence realized variance estimation

    NARCIS (Netherlands)

    Gatheral, J.; Oomen, R.C.A.

    2010-01-01

    Given a time series of intra-day tick-by-tick price data, how can realized variance be estimated? The obvious estimator—the sum of squared returns between trades—is biased by microstructure effects such as bid-ask bounce and so in the past, practitioners were advised to drop most of the data and

  15. FPGA Realization of Memory 10 Viterbi Decoder

    DEFF Research Database (Denmark)

    Paaske, Erik; Bach, Thomas Bo; Andersen, Jakob Dahl

    1997-01-01

    sequence mode when feedback from the Reed-Solomon decoder is available. The Viterbi decoder is realized using two Altera FLEX 10K50 FPGA's. The overall operating speed is 30 kbit/s, and since up to three iterations are performed for each frame and only one decoder is used, the operating speed...

  16. Evaluating realized genetic gains from tree improvement.

    Science.gov (United States)

    J.B. St. Clair

    1993-01-01

    Tree improvement has become an essential part of the management of forest lands for wood production, and predicting yields and realized gains from forests planted with genetically-improved trees will become increasingly important. This paper discusses concepts of tree improvement and genetic gain important to growth and yield modeling, and reviews previous studies of...

  17. Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and CoVolatility

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Lunde, Asger; Voev, Valeri

    We introduce a multivariate GARCH model that utilizes and models realized measures of volatility and covolatility. The realized measures extract information contained in high-frequency data that is particularly beneficial during periods with variation in volatility and covolatility. Applying the ...

  18. 5th Seminar on Stochastic Processes, Random Fields and Applications

    CERN Document Server

    Russo, Francesco; Dozzi, Marco

    2008-01-01

    This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: Y. Asai, J.-P. Aubin, C. Becker, M. Benaïm, H. Bessaih, S. Biagini, S. Bonaccorsi, N. Bouleau, N. Champagnat, G. Da Prato, R. Ferrière, F. Flandoli, P. Guasoni, V.B. Hallulli, D. Khoshnevisan, T. Komorowski, R. Léandre, P. Lescot, H. Lisei, J.A. López-Mimbela, V. Mandrekar, S. Méléard, A. Millet, H. Nagai, A.D. Neate, V. Orlovius, M. Pratelli, N. Privault, O. Raimond, M. Röckner, B. Rüdiger, W.J. Runggaldi...

  19. STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

    International Nuclear Information System (INIS)

    Johnson, Michael D.

    2016-01-01

    Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

  20. STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, Michael D., E-mail: mjohnson@cfa.harvard.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)

    2016-12-10

    Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

  1. Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Huang, Zhuo (Albert); Shek, Howard Howan

    GARCH models have been successful in modeling financial returns. Still, much is to be gained by incorporating a realized measure of volatility in these models. In this paper we introduce a new framework for the joint modeling of returns and realized measures of volatility. The Realized GARCH...... framework nests most GARCH models as special cases and is, in many ways, a natural extension of standard GARCH models. We pay special attention to linear and log-linear Realized GARCH specifications. This class of models has several attractive features. It retains the simplicity and tractability...... to latent volatility. This equation facilitates a simple modeling of the dependence between returns and future volatility that is commonly referred to as the leverage effect. An empirical application with DJIA stocks and an exchange traded index fund shows that a simple Realized GARCH structure leads...

  2. Hybrid approaches for multiple-species stochastic reaction–diffusion models

    International Nuclear Information System (INIS)

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

    2015-01-01

    Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries

  3. Hybrid approaches for multiple-species stochastic reaction–diffusion models

    Energy Technology Data Exchange (ETDEWEB)

    Spill, Fabian, E-mail: fspill@bu.edu [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Alarcon, Tomas [Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Maini, Philip K. [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Byrne, Helen [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD (United Kingdom)

    2015-10-15

    Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.

  4. Portfolio Management with Stochastic Interest Rates and Inflation Ambiguity

    DEFF Research Database (Denmark)

    Munk, Claus; Rubtsov, Alexey Vladimirovich

    We solve a stock-bond-cash portfolio choice problem for a risk- and ambiguity-averse investor in a setting where the inflation rate and interest rates are stochastic. The expected inflation rate is unobservable, but the investor may learn about it from realized inflation and observed stock and bond......-Jacobi-Bellman equation in closed form and derive and illustrate a number of interesting properties of the solution. For example, ambiguity aversion affects the optimal portfolio through the correlation of price level with the stock index, a bond, and the expected inflation rate. Furthermore, unlike other settings...

  5. Stochastic models: theory and simulation.

    Energy Technology Data Exchange (ETDEWEB)

    Field, Richard V., Jr.

    2008-03-01

    Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.

  6. Stochastic Still Water Response Model

    DEFF Research Database (Denmark)

    Friis-Hansen, Peter; Ditlevsen, Ove Dalager

    2002-01-01

    In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...

  7. Stochastic quantization of Einstein gravity

    International Nuclear Information System (INIS)

    Rumpf, H.

    1986-01-01

    We determine a one-parameter family of covariant Langevin equations for the metric tensor of general relativity corresponding to DeWitt's one-parameter family of supermetrics. The stochastic source term in these equations can be expressed in terms of a Gaussian white noise upon the introduction of a stochastic tetrad field. The only physically acceptable resolution of a mathematical ambiguity in the ansatz for the source term is the adoption of Ito's calculus. By taking the formal equilibrium limit of the stochastic metric a one-parameter family of covariant path-integral measures for general relativity is obtained. There is a unique parameter value, distinguished by any one of the following three properties: (i) the metric is harmonic with respect to the supermetric, (ii) the path-integral measure is that of DeWitt, (iii) the supermetric governs the linearized Einstein dynamics. Moreover the Feynman propagator corresponding to this parameter is causal. Finally we show that a consistent stochastic perturbation theory gives rise to a new type of diagram containing ''stochastic vertices.''

  8. NIM Realization of the Gallium Triple Point

    Science.gov (United States)

    Xiaoke, Yan; Ping, Qiu; Yuning, Duan; Yongmei, Qu

    2003-09-01

    In the last three years (1999 to 2001), the gallium triple-point cell has been successfully developed, and much corresponding research has been carried out at the National Institute of Metrology (NIM), Beijing, China. This paper presents the cell design, apparatus and procedure for realizing the gallium triple point, and presents studies on the different freezing methods. The reproducibility is 0.03 mK, and the expanded uncertainty of realization of the gallium triple point is evaluated to be 0.17 mK (p=0.99, k=2.9). Also, the reproducibility of the gallium triple point was compared with that of the triple point of water.

  9. Enablers & Barriers for Realizing Modularity Benefits

    DEFF Research Database (Denmark)

    Storbjerg, Simon Haahr; Brunø, Thomas Ditlev; Thyssen, Jesper

    2012-01-01

    far less attention compared to the theories and methods concerning modularization of technical systems. Harvesting the full potential of modularization, particularly in relation to product development agility, depends on more than an optimal architecture. Key enablers in this context......Although modularization is becoming both a well-described domain in academia and a broadly applied concept in business, many of today’s firm still struggle to realize the promised benefits of this approach. Managing modularization is a complex matter, and in spite of this, a topic that has received...... are the organizational and systems related aspects. Recognizing the need for guidance to realize the benefits of modularity, the purpose of this study is through a literature study and a case study to improve the insight into the organizational and systems related enablers and barriers with regard to obtaining the full...

  10. Exploring heterogeneous market hypothesis using realized volatility

    Science.gov (United States)

    Chin, Wen Cheong; Isa, Zaidi; Mohd Nor, Abu Hassan Shaari

    2013-04-01

    This study investigates the heterogeneous market hypothesis using high frequency data. The cascaded heterogeneous trading activities with different time durations are modelled by the heterogeneous autoregressive framework. The empirical study indicated the presence of long memory behaviour and predictability elements in the financial time series which supported heterogeneous market hypothesis. Besides the common sum-of-square intraday realized volatility, we also advocated two power variation realized volatilities in forecast evaluation and risk measurement in order to overcome the possible abrupt jumps during the credit crisis. Finally, the empirical results are used in determining the market risk using the value-at-risk approach. The findings of this study have implications for informationally market efficiency analysis, portfolio strategies and risk managements.

  11. Ecological advantages of partial migration as a conditional strategy.

    Science.gov (United States)

    Vélez-Espino, Luis A; McLaughlin, Robert L; Robillard, Melissa

    2013-05-01

    Partial migration is a widespread phenomenon characterized by migrant and resident forms from the same population. In phenotypically plastic taxa with indeterminate growth, resident and migrant ecophenotypes can differ in size and life history traits in ways expected to maximize fitness in the different habitats they exploit. Studies of partial migration in different taxa have advocated either density-dependence or environmental stochasticity as explanations for partial migration. We used a demographic approach for a virtual Brook Trout population to demonstrate the ecological consequences of partial migration under interacting density dependence and environmental stochasticity. The maintenance of partial migration as a conditional strategy in species/populations where resident and migrant forms exhibit life history asymmetries provides ecological advantages. We show that density-dependent migration is expected to increase population fitness under constant environmental conditions or low environmental variation, but decreases population fitness under high environmental variation. These conditions favor intermediate levels of migration as an advantageous tactic. However, there are threshold rates of return migration below which partial migration is no longer a viable tactic. Our modeling approach also allowed the exploration of the distribution of the population by life stage and habitat in response to the strength of density dependence, costs of migration, and return rates, and demonstrated the importance of the conservation of ecophenotypes in partially migratory populations. Copyright © 2013 Elsevier Inc. All rights reserved.

  12. Realization of superconductive films by screen printing

    International Nuclear Information System (INIS)

    Baudry, H.

    1988-01-01

    Screen printing is a promising method to manufacture superconductive lines making use of superconductive ceramics. An ink has been realized with YBa 2 Cu 3 0 7-x' and the process conditions defined by thermal analysis. A superconductive transition is observed after screen printing on MgO. The firing of the layer is made at 920 0 C followed by a reoxidation step at 420 0 C. The silver electrical contacts are also screen printed [fr

  13. New techniques used to realize silicon photocells

    International Nuclear Information System (INIS)

    Siffert, P.

    1978-01-01

    The techniques used to realize the terrestrial silicon solar cells being considered the possible improvements of these methods are discussed. The various approaches under development to prepare silicon sheets in a continuous way are considered for both self-supporting or substrate deposited layers. Finally, the various methods used or under investigation to obtain the surface potential barrier are considered; MIS, heterojunction and ion implantation [fr

  14. Experimental functional realization of attribute grammar system

    Directory of Open Access Journals (Sweden)

    I. Attali

    2002-07-01

    Full Text Available In this paper we present an experimental functional realization of attribute grammar(AG system for personal computers. For AG system functioning only Turbo Prolog compiler is required. The system functioning is based on a specially elaborated metalanguage for AG description, universal syntactic and semantic constructors. The AG system provides automatic generation of target compiler (syntax--oriented software using Turbo Prolog as object language.

  15. Solution of stochastic media transport problems using a numerical quadrature-based method

    International Nuclear Information System (INIS)

    Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.

    2013-01-01

    We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)

  16. Stochastic dynamics modeling solute transport in porous media modeling solute transport in porous media

    CERN Document Server

    Kulasiri, Don

    2002-01-01

    Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...

  17. Oil shale mines and their realizable production

    International Nuclear Information System (INIS)

    Habicht, K.

    1994-01-01

    The production of Estonian oil shale depends on its marketing opportunities. The realizable production is a function of the oil shale price, which in turn depends on production costs. The latter are dependent on which mines are producing oil shale and on the volume of production. The purpose of the present article is to analyze which mines should operate under various realizable production scenarios and what should be their annual output so that the total cost of oil shale production (including maintenance at idle mines) is minimized. This paper is also targeted at observing the change in the average production cost per ton of oil shale depending on the realizable output. The calculations are based on data for the first four months of 1993, as collected by N. Barabaner (Estonian Academy of Sciences, Institute of Economy). The data include the total production volume and production cost from the mines of RE 'Eesti Polevkivi' (State Enterprise 'Estonian Oil Shale'). They also project expenses from mine closings in case of conservation. The latter costs were allocated among mines in direct proportion to their respective number of employees. (author)

  18. Coset realization of unifying W-algebras

    International Nuclear Information System (INIS)

    Blumenhagen, R.; Huebel, R.

    1994-06-01

    We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R)/sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as 'WD -n '. In addition, minimal models of WD -n are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras. (orig.)

  19. Dynamic large eddy simulation: Stability via realizability

    Science.gov (United States)

    Mokhtarpoor, Reza; Heinz, Stefan

    2017-10-01

    The concept of dynamic large eddy simulation (LES) is highly attractive: such methods can dynamically adjust to changing flow conditions, which is known to be highly beneficial. For example, this avoids the use of empirical, case dependent approximations (like damping functions). Ideally, dynamic LES should be local in physical space (without involving artificial clipping parameters), and it should be stable for a wide range of simulation time steps, Reynolds numbers, and numerical schemes. These properties are not trivial, but dynamic LES suffers from such problems over decades. We address these questions by performing dynamic LES of periodic hill flow including separation at a high Reynolds number Re = 37 000. For the case considered, the main result of our studies is that it is possible to design LES that has the desired properties. It requires physical consistency: a PDF-realizable and stress-realizable LES model, which requires the inclusion of the turbulent kinetic energy in the LES calculation. LES models that do not honor such physical consistency can become unstable. We do not find support for the previous assumption that long-term correlations of negative dynamic model parameters are responsible for instability. Instead, we concluded that instability is caused by the stable spatial organization of significant unphysical states, which are represented by wall-type gradient streaks of the standard deviation of the dynamic model parameter. The applicability of our realizability stabilization to other dynamic models (including the dynamic Smagorinsky model) is discussed.

  20. Realization of logical functions by vector programs

    Energy Technology Data Exchange (ETDEWEB)

    Lapkin, L Ya

    1983-03-01

    Recent computing and control applications often require program realization of finite automata in general and of an important particular class of memoryless automata specified by systems of Boolean functions. Logical control and computing machines which receive sequences of discrete signals on the input and convert them into sequences of discrete output signals using finite memory may be described by a finite automation model. However, in distinction from the circuit interpretation of finite automata, the automaton algorithm represents the structure of the automaton program and not the structure of the machine itself. Therefore, the complexity of the computer realization of an automaton is the complexity of the computer program, and not the complexity of the hardware. Two classes of programs currently used to evalute boolean functions are operator programs and binary programs. However, computing machines, including microcomputers, are equipped with additional possibilities for evaluation of Boolean functions, which are not utilized in programs of these two basic classes. In this article, we consider the design of vector programs for program realization of systems of Boolean functions. 3 references.

  1. Realization of chiral symmetry in the ERG

    International Nuclear Information System (INIS)

    Echigo, Yoshio; Igarashi, Yuji

    2011-01-01

    We discuss within the framework of the ERG how chiral symmetry is realized in a linear σ model. A generalized Ginsparg-Wilson relation is obtained from the Ward-Takahashi identities for the Wilson action assumed to be bilinear in the Dirac fields. We construct a family of its non-perturbative solutions. The family generates the most general solutions to the Ward-Takahashi identities. Some special solutions are discussed. For each solution in this family, chiral symmetry is realized in such a way that a change in the Wilson action under non-linear symmetry transformation is canceled with a change in the functional measure. We discuss that the family of solutions reduces via a field redefinition to a family of the Wilson actions with some composite object of the scalar fields which has a simple transformation property. For this family, chiral symmetry is linearly realized with a continuum analog of the operator extension of γ 5 used on the lattice. We also show that there exist some appropriate Dirac fields which obey the standard chiral transformations with γ 5 in contrast to the lattice case. Their Yukawa interaction with scalars, however, becomes non-linear. (author)

  2. Rainfall Stochastic models

    Science.gov (United States)

    Campo, M. A.; Lopez, J. J.; Rebole, J. P.

    2012-04-01

    This work was carried out in north of Spain. San Sebastian A meteorological station, where there are available precipitation records every ten minutes was selected. Precipitation data covers from October of 1927 to September of 1997. Pulse models describe the temporal process of rainfall as a succession of rainy cells, main storm, whose origins are distributed in time according to a Poisson process and a secondary process that generates a random number of cells of rain within each storm. Among different pulse models, the Bartlett-Lewis was used. On the other hand, alternative renewal processes and Markov chains describe the way in which the process will evolve in the future depending only on the current state. Therefore they are nor dependant on past events. Two basic processes are considered when describing the occurrence of rain: the alternation of wet and dry periods and temporal distribution of rainfall in each rain event, which determines the rainwater collected in each of the intervals that make up the rain. This allows the introduction of alternative renewal processes and Markov chains of three states, where interstorm time is given by either of the two dry states, short or long. Thus, the stochastic model of Markov chains tries to reproduce the basis of pulse models: the succession of storms, each one composed for a series of rain, separated by a short interval of time without theoretical complexity of these. In a first step, we analyzed all variables involved in the sequential process of the rain: rain event duration, event duration of non-rain, average rainfall intensity in rain events, and finally, temporal distribution of rainfall within the rain event. Additionally, for pulse Bartlett-Lewis model calibration, main descriptive statistics were calculated for each month, considering the process of seasonal rainfall in each month. In a second step, both models were calibrated. Finally, synthetic series were simulated with calibration parameters; series

  3. Stacking with stochastic cooling

    Energy Technology Data Exchange (ETDEWEB)

    Caspers, Fritz E-mail: Fritz.Caspers@cern.ch; Moehl, Dieter

    2004-10-11

    Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 10{sup 5} the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some

  4. Stochastic models of cell motility

    DEFF Research Database (Denmark)

    Gradinaru, Cristian

    2012-01-01

    Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...

  5. Stochastic Modelling of Hydrologic Systems

    DEFF Research Database (Denmark)

    Jonsdottir, Harpa

    2007-01-01

    In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....

  6. Stochastic quantization of general relativity

    International Nuclear Information System (INIS)

    Rumpf, H.

    1986-01-01

    Following an elementary exposition of the basic mathematical concepts used in the theory of stochastic relaxation processes the stochastic quantization method of Parisi and Wu is briefly reviewed. The method is applied to Einstein's theory of gravitation using a formalism that is manifestly covariant with respect to field redefinitions. This requires the adoption of Ito's calculus and the introduction of a metric in field configuration space, for which there is a unique candidate. Due to the indefiniteness of the Euclidean Einstein-Hilbert action stochastic quantization is generalized to the pseudo-Riemannian case. It is formally shown to imply the DeWitt path integral measure. Finally a new type of perturbation theory is developed. (Author)

  7. Applied probability and stochastic processes

    CERN Document Server

    Sumita, Ushio

    1999-01-01

    Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...

  8. Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

    KAUST Repository

    El-Beltagy, Mohamed A.; Al-Juhani, Amnah

    2015-01-01

    Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

  9. Stochastic approach and fluctuation theorem for charge transport in diodes

    Science.gov (United States)

    Gu, Jiayin; Gaspard, Pierre

    2018-05-01

    A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

  10. Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

    KAUST Repository

    El-Beltagy, Mohamed A.

    2015-01-07

    Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

  11. Nonlinear Stochastic Analysis of Subharmonic Response of a Shallow Cable

    DEFF Research Database (Denmark)

    Zhou, Q.; Stærdahl, Jesper Winther; Nielsen, Søren R.K.

    2007-01-01

    and stochastic subharmonic response is demonstrated upon comparison with a more involved model based on a spatial finite difference discretization of the full nonlinear partial differential equations of the cable. Since the stochastic response quantities are obtained by Monte Carlo simulation, which is extremely...... time-consuming for the finite difference model, most of the results are next based on the reduced model. Under harmonical varying support point motions the stable subharmonic motion consists of a harmonically varying component in the equilibrium plane and a large subharmonic out-of-plane component...... subharmonic response component is also present in the static equilibrium plane. Further, the time variation of the envelope process of the narrow-banded chordwise elongation process tends to enhance chaotic behaviour of the subharmonic response, which is detectable via extreme sensitivity on the initial...

  12. Stochastic geometry for image analysis

    CERN Document Server

    Descombes, Xavier

    2013-01-01

    This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are  described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed.  Numerous applications, covering remote sensing images, biological and medical imaging, are detailed.  This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.

  13. Stochastic methods in quantum mechanics

    CERN Document Server

    Gudder, Stanley P

    2005-01-01

    Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun

  14. STOCHASTIC METHODS IN RISK ANALYSIS

    Directory of Open Access Journals (Sweden)

    Vladimíra OSADSKÁ

    2017-06-01

    Full Text Available In this paper, we review basic stochastic methods which can be used to extend state-of-the-art deterministic analytical methods for risk analysis. We can conclude that the standard deterministic analytical methods highly depend on the practical experience and knowledge of the evaluator and therefore, the stochastic methods should be introduced. The new risk analysis methods should consider the uncertainties in input values. We present how large is the impact on the results of the analysis solving practical example of FMECA with uncertainties modelled using Monte Carlo sampling.

  15. Stochastic dynamics of new inflation

    International Nuclear Information System (INIS)

    Nakao, Ken-ichi; Nambu, Yasusada; Sasaki, Misao.

    1988-07-01

    We investigate thoroughly the dynamics of an inflation-driving scalar field in terms of an extended version of the stochastic approach proposed by Starobinsky and discuss the spacetime structure of the inflationary universe. To avoid any complications which might arise due to quantum gravity, we concentrate our discussions on the new inflationary universe scenario in which all the energy scales involved are well below the planck mass. The investigation is done both analytically and numerically. In particular, we present a full numerical analysis of the stochastic scalar field dynamics on the phase space. Then implications of the results are discussed. (author)

  16. Stochastic mechanics and quantum theory

    International Nuclear Information System (INIS)

    Goldstein, S.

    1987-01-01

    Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic) physical reality. Stochastic mechanics presents a unified treatment of the microscopic and macroscopic domains, in which the process of measurement plays no special physical role and which reduces to Newtonian mechanics in the macroscopic limit

  17. Probability, Statistics, and Stochastic Processes

    CERN Document Server

    Olofsson, Peter

    2011-01-01

    A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d

  18. QB1 - Stochastic Gene Regulation

    Energy Technology Data Exchange (ETDEWEB)

    Munsky, Brian [Los Alamos National Laboratory

    2012-07-23

    Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.

  19. Stochastic geometry and its applications

    CERN Document Server

    Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph

    2013-01-01

    An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a

  20. Algebraic and stochastic coding theory

    CERN Document Server

    Kythe, Dave K

    2012-01-01

    Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.

  1. Stochastic and infinite dimensional analysis

    CERN Document Server

    Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José

    2016-01-01

    This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.

  2. A Fractionally Integrated Wishart Stochastic Volatility Model

    NARCIS (Netherlands)

    M. Asai (Manabu); M.J. McAleer (Michael)

    2013-01-01

    textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

  3. Exact Algorithms for Solving Stochastic Games

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels

    2012-01-01

    Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

  4. Transport properties of stochastic Lorentz models

    NARCIS (Netherlands)

    Beijeren, H. van

    Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed

  5. Theory, technology, and technique of stochastic cooling

    International Nuclear Information System (INIS)

    Marriner, J.

    1993-10-01

    The theory and technological implementation of stochastic cooling is described. Theoretical and technological limitations are discussed. Data from existing stochastic cooling systems are shown to illustrate some useful techniques

  6. Partial tooth gear bearings

    Science.gov (United States)

    Vranish, John M. (Inventor)

    2010-01-01

    A partial gear bearing including an upper half, comprising peak partial teeth, and a lower, or bottom, half, comprising valley partial teeth. The upper half also has an integrated roller section between each of the peak partial teeth with a radius equal to the gear pitch radius of the radially outwardly extending peak partial teeth. Conversely, the lower half has an integrated roller section between each of the valley half teeth with a radius also equal to the gear pitch radius of the peak partial teeth. The valley partial teeth extend radially inwardly from its roller section. The peak and valley partial teeth are exactly out of phase with each other, as are the roller sections of the upper and lower halves. Essentially, the end roller bearing of the typical gear bearing has been integrated into the normal gear tooth pattern.

  7. Numerical computation of the transport matrix in toroidal plasma with a stochastic magnetic field

    Science.gov (United States)

    Zhu, Siqiang; Chen, Dunqiang; Dai, Zongliang; Wang, Shaojie

    2018-04-01

    A new numerical method, based on integrating along the full orbit of guiding centers, to compute the transport matrix is realized. The method is successfully applied to compute the phase-space diffusion tensor of passing electrons in a tokamak with a stochastic magnetic field. The new method also computes the Lagrangian correlation function, which can be used to evaluate the Lagrangian correlation time and the turbulence correlation length. For the case of the stochastic magnetic field, we find that the order of magnitude of the parallel correlation length can be estimated by qR0, as expected previously.

  8. Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection

    Directory of Open Access Journals (Sweden)

    Gabriel Martos

    2018-01-01

    Full Text Available We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to estimate minimum entropy sets. These sets are relevant to detect anomalous or outlier functional data. A numerical experiment illustrates the performance of the proposed method; in addition, we conduct an analysis of mortality rate curves as an interesting application in a real-data context to explore functional anomaly detection.

  9. Stochastic modeling and analysis of telecoms networks

    CERN Document Server

    Decreusefond, Laurent

    2012-01-01

    This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an

  10. Dynamical and hamiltonian dilations of stochastic processes

    International Nuclear Information System (INIS)

    Baumgartner, B.; Gruemm, H.-R.

    1982-01-01

    This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)

  11. Essays on partial retirement

    NARCIS (Netherlands)

    Kantarci, T.

    2012-01-01

    The five essays in this dissertation address a range of topics in the micro-economic literature on partial retirement. The focus is on the labor market behavior of older age groups. The essays examine the economic and non-economic determinants of partial retirement behavior, the effect of partial

  12. Abstract probabilistic CNOT gate model based on double encoding: study of the errors and physical realizability

    Science.gov (United States)

    Gueddana, Amor; Attia, Moez; Chatta, Rihab

    2015-03-01

    In this work, we study the error sources standing behind the non-perfect linear optical quantum components composing a non-deterministic quantum CNOT gate model, which performs the CNOT function with a success probability of 4/27 and uses a double encoding technique to represent photonic qubits at the control and the target. We generalize this model to an abstract probabilistic CNOT version and determine the realizability limits depending on a realistic range of the errors. Finally, we discuss physical constraints allowing the implementation of the Asymmetric Partially Polarizing Beam Splitter (APPBS), which is at the heart of correctly realizing the CNOT function.

  13. Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information

    NARCIS (Netherlands)

    Postek, Krzysztof; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

    2015-01-01

    In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD).

  14. Double diffusivity model under stochastic forcing

    Science.gov (United States)

    Chattopadhyay, Amit K.; Aifantis, Elias C.

    2017-05-01

    The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

  15. A stochastic aerodynamic model for stationary blades in unsteady 3D wind fields

    International Nuclear Information System (INIS)

    Fluck, Manuel; Crawford, Curran

    2016-01-01

    Dynamic loads play an important roll in the design of wind turbines, but establishing the life-time aerodynamic loads (e.g. extreme and fatigue loads) is a computationally expensive task. Conventional (deterministic) methods to analyze long term loads, which rely on the repeated analysis of multiple different wind samples, are usually too expensive to be included in optimization routines. We present a new stochastic approach, which solves the aerodynamic system equations (Lagrangian vortex model) in the stochastic space, and thus arrive directly at a stochastic description of the coupled loads along a turbine blade. This new approach removes the requirement of analyzing multiple different realizations. Instead, long term loads can be extracted from a single stochastic solution, a procedure that is obviously significantly faster. Despite the reduced analysis time, results obtained from the stochastic approach match deterministic result well for a simple test-case (a stationary blade). In future work, the stochastic method will be extended to rotating blades, thus opening up new avenues to include long term loads into turbine optimization. (paper)

  16. Environmental vs Demographic Stochasticity in Population Growth

    OpenAIRE

    Braumann, C. A.

    2010-01-01

    Compares the effect on population growth of envinonmental stochasticity (random environmental variations described by stochastic differential equations) with demographic stochasticity (random variations in births and deaths described by branching processes and birth-and-death processes), in the density-independent and the density-dependent cases.

  17. Stochastic diffusion models for substitutable technological innovations

    NARCIS (Netherlands)

    Wang, L.; Hu, B.; Yu, X.

    2004-01-01

    Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the

  18. Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

    Directory of Open Access Journals (Sweden)

    A. Valor

    2013-01-01

    Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

  19. Distributed EMPC of multiple microgrids for coordinated stochastic energy management

    International Nuclear Information System (INIS)

    Kou, Peng; Liang, Deliang; Gao, Lin

    2017-01-01

    Highlights: • Reducing the system wide operating cost compared to the no-cooperation energy management strategy. • Maintaining the supply and demand balance within each microgrid. • Handling the uncertainties in both supply and demand. • Converting the stochastic optimization problems to standard quadratic and linear programming problems. • Achieving a good balance between control performance and computationally feasibility. - Abstract: The concept of multi-microgrids has the potential to improve the reliability and economic performance of a distribution system. To realize this potential, a coordination among multiple microgrids is needed. In this context, this paper presents a new distributed economic model predictive control scheme for the coordinated stochastic energy management of multi-microgrids. By optimally coordinating the operation of individual microgrids, this scheme maintains the system-wide supply and demand balance in an economical manner. Based on the probabilistic forecasts of renewable power generation and microgrid load, this scheme effectively handles the uncertainties in both supply and demand. Using the Chebyshev inequality and the Delta method, the corresponding stochastic optimization problems have been converted to quadratic and linear programs. The proposed scheme is evaluated on a large-scale case that includes ten interconnected microgrids. The results indicated that the proposed scheme successfully reduces the system wide operating cost, achieves the supply-demand balance in each microgrid, and brings the energy exchange between DNO and main grid to a predefined trajectory.

  20. Development of stochastic indicator models of lithology, Yucca Mountain, Nevada

    International Nuclear Information System (INIS)

    Rautman, C.A.; Robey, T.H.

    1994-01-01

    Indicator geostatistical techniques have been used to produce a number of fully three-dimensional stochastic simulations of large-scale lithologic categories at the Yucca Mountain site. Each realization reproduces the available drill hole data used to condition the simulation. Information is propagated away from each point of observation in accordance with a mathematical model of spatial continuity inferred through soft data taken from published geologic cross sections. Variations among the simulated models collectively represent uncertainty in the lithology at unsampled locations. These stochastic models succeed in capturing many major features of welded-nonwelded lithologic framework of Yucca Mountain. However, contacts between welded and nonwelded rock types for individual simulations appear more complex than suggested by field observation, and a number of probable numerical artifacts exist in these models. Many of the apparent discrepancies between the simulated models and the general geology of Yucca Mountain represent characterization uncertainty, and can be traced to the sparse site data used to condition the simulations. Several vertical stratigraphic columns have been extracted from the three-dimensional stochastic models for use in simplified total-system performance assessment exercises. Simple, manual adjustments are required to eliminate the more obvious simulation artifacts and to impose a secondary set of deterministic geologic features on the overall stratigraphic framework provided by the indictor models

  1. APM Best Practices Realizing Application Performance Management

    CERN Document Server

    Sydor, Michael J

    2011-01-01

    The objective of APM Best Practices: Realizing Application Performance Management is to establish reliable application performance management (APM) practices - to demonstrate value, to do it quickly, and to adapt to the client circumstances. It's important to balance long-term goals with short-term deliverables, but without compromising usefulness or correctness. The successful strategy is to establish a few reasonable goals, achieve them quickly, and then iterate over the same topics two more times, with each successive iteration expanding the skills and capabilities of the APM team. This str

  2. Analysis of Popper's Experiment and Its Realization

    Science.gov (United States)

    Qureshi, T.

    2012-04-01

    An experiment proposed by Karl Popper to test the standard interpretation of quantum mechanics was realized by Kim and Shih. We use a quantum mechanical calculation to analyze Popper's proposal, and find a surprising result for the location of the virtual slit. We also analyze Kim and Shih's experiment, and demonstrate that although it ingeniously overcomes the problem of temporal spreading of the wave-packet, it is inconclusive about Popper's test. We point out that another experiment which (unknowingly) implements Popper's test in a conclusive way, has actually been carried out. Its results are in contradiction with Popper's prediction, and agree with our analysis.

  3. Quantization of a nonlinearly realized supersymmetric theory

    International Nuclear Information System (INIS)

    Shima, K.

    1977-01-01

    The two-dimensional version of the Volkov-Akulov Lagrangian, where the supersymmetry is realized nonlinearly by means of a single Majorana spinor psi (x), is quantized. The equal-time anticommutators for the field are not c numbers but are functions of the field itself. By explicit calculation we shall show that the supersymmetry charges of the model form the supersymmetry algebra (the graded Lie algebra); therefore the Hamiltonian of the system P 0 is written as a bilinear sum of products of supersymmetry charges. We shall also show that the supersymmetry charges exactly generate a constant translation of psi (x) in the spinor space

  4. Perturbation theory from stochastic quantization

    International Nuclear Information System (INIS)

    Hueffel, H.

    1984-01-01

    By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)

  5. Stochastic Modelling of River Geometry

    DEFF Research Database (Denmark)

    Sørensen, John Dalsgaard; Schaarup-Jensen, K.

    1996-01-01

    Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....

  6. Stochastic Processes in Epidemic Theory

    CERN Document Server

    Lefèvre, Claude; Picard, Philippe

    1990-01-01

    This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.

  7. Stochastic theory of grain growth

    International Nuclear Information System (INIS)

    Hu Haiyun; Xing Xiusan.

    1990-11-01

    The purpose of this note is to set up a stochastic theory of grain growth and to derive the statistical distribution function and the average value of the grain radius so as to match them with the experiment further. 8 refs, 1 fig

  8. Stochastic vehicle routing with recourse

    DEFF Research Database (Denmark)

    Gørtz, Inge Li; Nagarajan, Viswanath; Saket, Rishi

    2012-01-01

    instantiations, a recourse route is computed - but costs here become more expensive by a factor λ. We present an O(log2n ·log(nλ))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular...

  9. Universality in stochastic exponential growth.

    Science.gov (United States)

    Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

    2014-07-11

    Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

  10. Stochastic control of traffic patterns

    DEFF Research Database (Denmark)

    Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer

    2013-01-01

    A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage of h...

  11. The fermion stochastic calculus I

    International Nuclear Information System (INIS)

    Streater, R.F.

    1984-01-01

    The author describes the stochastic calculus of quantum processes with fermions. After a description of the Clifford algebra as the csup(*)-algebra generated by spinor fields the damped harmonic oscillator with quantum noise is considered as example. Then the Clifford process is described. Finally the Ito-Clifford integral and the Ito-Clifford isometry are presented. (HSI)

  12. Stochastic and Chaotic Relaxation Oscillations

    NARCIS (Netherlands)

    Grasman, J.; Roerdink, J.B.T.M.

    1988-01-01

    For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a

  13. Stochastic processes in mechanical engineering

    NARCIS (Netherlands)

    Brouwers, J.J.H.

    2006-01-01

    Stochastic or random vibrations occur in a variety of applications of mechanicalengineering. Examples are: the dynamics of a vehicle on an irregular roadsurface; the variation in time of thermodynamic variables in municipal wasteincinerators due to fluctuations in heating value of the waste; the

  14. Testing for Stochastic Dominance Efficiency

    NARCIS (Netherlands)

    G.T. Post (Thierry); O. Linton; Y-J. Whang

    2005-01-01

    textabstractWe propose a new test of the stochastic dominance efficiency of a given portfolio over a class of portfolios. We establish its null and alternative asymptotic properties, and define a method for consistently estimating critical values. We present some numerical evidence that our

  15. Network Analysis with Stochastic Grammars

    Science.gov (United States)

    2015-09-17

    rules N = 0 //non-terminal index clusters = cluster(W) //number of clusters drive the number S productions //cluster function described in text...Essa, “Recognizing multitasked activities from video using stochastic context-free grammar,” AAAI/IAAI, pp. 770–776, 2002. [18] R. Nevatia, T. Zhao

  16. Stochastic Volatility and DSGE Models

    DEFF Research Database (Denmark)

    Andreasen, Martin Møller

    This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...

  17. American options under stochastic volatility

    NARCIS (Netherlands)

    Chockalingam, A.; Muthuraman, K.

    2011-01-01

    The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrate that volatility is not constant, and stochastic volatility models are used to account for dynamic volatility

  18. Stochastic cooling system in COSY

    International Nuclear Information System (INIS)

    Brittner, P.; Hacker, H.U.; Prasuhn, D.; Schug, G.; Singer, H.; Spiess, W.; Stassen, R.

    1994-01-01

    The stochastic cooler system in COSY is designed for proton kinetic energies between 0.8 and 2.5 GeV. Fabrication of the mechanical parts of the system is going on. Test results of the prototype measurements as well as data of the active RF-compontens are presented. (orig.)

  19. Stochastic cooling system in COSY

    Energy Technology Data Exchange (ETDEWEB)

    Brittner, P [Forschungszentrum Juelich GmbH (Germany); Hacker, H U [Forschungszentrum Juelich GmbH (Germany); Prasuhn, D [Forschungszentrum Juelich GmbH (Germany); Schug, G [Forschungszentrum Juelich GmbH (Germany); Singer, H [Forschungszentrum Juelich GmbH (Germany); Spiess, W [Forschungszentrum Juelich GmbH (Germany); Stassen, R [Forschungszentrum Juelich GmbH (Germany)

    1994-09-01

    The stochastic cooler system in COSY is designed for proton kinetic energies between 0.8 and 2.5 GeV. Fabrication of the mechanical parts of the system is going on. Test results of the prototype measurements as well as data of the active RF-compontens are presented. (orig.)

  20. Stochastic-field cavitation model

    International Nuclear Information System (INIS)

    Dumond, J.; Magagnato, F.; Class, A.

    2013-01-01

    Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations

  1. Stochastic-field cavitation model

    Science.gov (United States)

    Dumond, J.; Magagnato, F.; Class, A.

    2013-07-01

    Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

  2. Distance covariance for stochastic processes

    DEFF Research Database (Denmark)

    Matsui, Muneya; Mikosch, Thomas Valentin; Samorodnitsky, Gennady

    2017-01-01

    The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analog of the distance covariance for two stochastic processes...

  3. Multiscale study on stochastic reconstructions of shale samples

    Science.gov (United States)

    Lili, J.; Lin, M.; Jiang, W. B.

    2016-12-01

    Shales are known to have multiscale pore systems, composed of macroscale fractures, micropores, and nanoscale pores within gas or oil-producing organic material. Also, shales are fissile and laminated, and the heterogeneity in horizontal is quite different from that in vertical. Stochastic reconstructions are extremely useful in situations where three-dimensional information is costly and time consuming. Thus the purpose of our paper is to reconstruct stochastically equiprobable 3D models containing information from several scales. In this paper, macroscale and microscale images of shale structure in the Lower Silurian Longmaxi are obtained by X-ray microtomography and nanoscale images are obtained by scanning electron microscopy. Each image is representative for all given scales and phases. Especially, the macroscale is four times coarser than the microscale, which in turn is four times lower in resolution than the nanoscale image. Secondly, the cross correlation-based simulation method (CCSIM) and the three-step sampling method are combined together to generate stochastic reconstructions for each scale. It is important to point out that the boundary points of pore and matrix are selected based on multiple-point connectivity function in the sampling process, and thus the characteristics of the reconstructed image can be controlled indirectly. Thirdly, all images with the same resolution are developed through downscaling and upscaling by interpolation, and then we merge multiscale categorical spatial data into a single 3D image with predefined resolution (the microscale image). 30 realizations using the given images and the proposed method are generated. The result reveals that the proposed method is capable of preserving the multiscale pore structure, both vertically and horizontally, which is necessary for accurate permeability prediction. The variogram curves and pore-size distribution for both original 3D sample and the generated 3D realizations are compared

  4. An extension of clarke's model with stochastic amplitude flip processes

    KAUST Repository

    Hoel, Hakon

    2014-07-01

    Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.

  5. Recurrent Partial Words

    Directory of Open Access Journals (Sweden)

    Francine Blanchet-Sadri

    2011-08-01

    Full Text Available Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words. Given an infinite partial word w, the number of distinct full words over the alphabet that are compatible with factors of w of length n, called subwords of w, refers to a measure of complexity of infinite partial words so-called subword complexity. This measure is of particular interest because we can construct partial words with subword complexities not achievable by full words. In this paper, we consider the notion of recurrence over infinite partial words, that is, we study whether all of the finite subwords of a given infinite partial word appear infinitely often, and we establish connections between subword complexity and recurrence in this more general framework.

  6. Realization of fiber optic displacement sensors

    Science.gov (United States)

    Guzowski, Bartlomiej; Lakomski, Mateusz

    2018-03-01

    Fiber optic sensors are very promising because of their inherent advantages such as very small size, hard environment tolerance and impact of electromagnetic fields. In this paper three different types of Intensity Fiber Optic Displacement Sensors (I-FODS) are presented. Three configurations of I-FODS were realized in two varieties. In the first one, the cleaved multimode optical fibers (MMF) were used to collect reflected light, while in the second variety the MMF ended with ball lenses were chosen. To ensure an accurate alignment of optical fibers in the sensor head the MTP C9730 optical fiber ferrules were used. In this paper the influence of distribution of transmitting and detecting optical fibers on sensitivity and linear range of operation of developed I-FODS were investigated. We have shown, that I-FODS with ball lenses receive average 10.5% more reflected power in comparison to the cleaved optical fibers and they increase linearity range of I-FODS by 33%. In this paper, an analysis of each type of the realized sensor and detailed discussion are given.

  7. Realization of quantum Fourier transform over ZN

    International Nuclear Information System (INIS)

    Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao

    2014-01-01

    Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)

  8. Stochastic p -Bits for Invertible Logic

    Science.gov (United States)

    Camsari, Kerem Yunus; Faria, Rafatul; Sutton, Brian M.; Datta, Supriyo

    2017-07-01

    Conventional semiconductor-based logic and nanomagnet-based memory devices are built out of stable, deterministic units such as standard metal-oxide semiconductor transistors, or nanomagnets with energy barriers in excess of ≈40 - 60 kT . In this paper, we show that unstable, stochastic units, which we call "p -bits," can be interconnected to create robust correlations that implement precise Boolean functions with impressive accuracy, comparable to standard digital circuits. At the same time, they are invertible, a unique property that is absent in standard digital circuits. When operated in the direct mode, the input is clamped, and the network provides the correct output. In the inverted mode, the output is clamped, and the network fluctuates among all possible inputs that are consistent with that output. First, we present a detailed implementation of an invertible gate to bring out the key role of a single three-terminal transistorlike building block to enable the construction of correlated p -bit networks. The results for this specific, CMOS-assisted nanomagnet-based hardware implementation agree well with those from a universal model for p -bits, showing that p -bits need not be magnet based: any three-terminal tunable random bit generator should be suitable. We present a general algorithm for designing a Boltzmann machine (BM) with a symmetric connection matrix [J ] (Ji j=Jj i) that implements a given truth table with p -bits. The [J ] matrices are relatively sparse with a few unique weights for convenient hardware implementation. We then show how BM full adders can be interconnected in a partially directed manner (Ji j≠Jj i) to implement large logic operations such as 32-bit binary addition. Hundreds of stochastic p -bits get precisely correlated such that the correct answer out of 233 (≈8 ×1 09) possibilities can be extracted by looking at the statistical mode or majority vote of a number of time samples. With perfect directivity (Jj i=0 ) a small

  9. Research on nonlinear stochastic dynamical price model

    International Nuclear Information System (INIS)

    Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng

    2008-01-01

    In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies

  10. Stochastic volatility of volatility in continuous time

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole; Veraart, Almut

    This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility...... of volatility can be defined both non-parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated...

  11. Processes, mechanisms, parameters, and modeling approaches for partially saturated flow in soil and rock media

    International Nuclear Information System (INIS)

    Wang, J.S.Y.; Narasimhan, T.N.

    1993-06-01

    This report discusses conceptual models and mathematical equations, analyzes distributions and correlations among hydrological parameters of soils and tuff, introduces new path integration approaches, and outlines scaling procedures to model potential-driven fluid flow in heterogeneous media. To properly model the transition from fracture-dominated flow under saturated conditions to matrix-dominated flow under partially saturated conditions, characteristic curves and permeability functions for fractures and matrix need to be improved and validated. Couplings from two-phase flow, heat transfer, solute transport, and rock deformation to liquid flow are also important. For stochastic modeling of alternating units of welded and nonwelded tuff or formations bounded by fault zones, correlations and constraints on average values of saturated permeability and air entry scaling factor between different units need to be imposed to avoid unlikely combinations of parameters and predictions. Large-scale simulations require efficient and verifiable numerical algorithms. New path integration approaches based on postulates of minimum work and mass conservation to solve flow geometry and potential distribution simultaneously are introduced. This verifiable integral approach, together with fractal scaling procedures to generate statistical realizations with parameter distribution, correlation, and scaling taken into account, can be used to quantify uncertainties and generate the cumulative distribution function for groundwater travel times

  12. Simulation of Stochastic Processes by Coupled ODE-PDE

    Science.gov (United States)

    Zak, Michail

    2008-01-01

    A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

  13. xSPDE: Extensible software for stochastic equations

    Directory of Open Access Journals (Sweden)

    Simon Kiesewetter

    2016-01-01

    Full Text Available We introduce an extensible software toolbox, xSPDE, for solving ordinary and partial stochastic differential equations. The toolbox makes extensive use of vector and parallel methods. Inputs are exceptionally simple, to reduce the learning curve, with default options for all of the many input parameters. The code calculates functional means, correlations and spectra, checks for errors in both time-step and sampling, and provides several choices of algorithm. Most aspects of the code, including the numerical algorithm, have a modular functional design to allow user modifications.

  14. Stochastic Reachability Analysis of Hybrid Systems

    CERN Document Server

    Bujorianu, Luminita Manuela

    2012-01-01

    Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...

  15. Momentum Maps and Stochastic Clebsch Action Principles

    Science.gov (United States)

    Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

    2018-01-01

    We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

  16. Compatriot partiality and cosmopolitan justice: Can we justify compatriot partiality within the cosmopolitan framework?

    Directory of Open Access Journals (Sweden)

    Rachelle Bascara

    2016-10-01

    Full Text Available This paper shows an alternative way in which compatriot partiality could be justified within the framework of global distributive justice. Philosophers who argue that compatriot partiality is similar to racial partiality capture something correct about compatriot partiality. However, the analogy should not lead us to comprehensively reject compatriot partiality. We can justify compatriot partiality on the same grounds that liberation movements and affirmative action have been justified. Hence, given cosmopolitan demands of justice, special consideration for the economic well-being of your nation as a whole is justified if and only if the country it identifies is an oppressed developing nation in an unjust global order.This justification is incomplete. We also need to say why Person A, qua national of Country A, is justified in helping her compatriots in Country A over similarly or slightly more oppressed non-compatriots in Country B. I argue that Person A’s partiality towards her compatriots admits further vindication because it is part of an oppressed group’s project of self-emancipation, which is preferable to paternalistic emancipation.Finally, I identify three benefits in my justification for compatriot partiality. First, I do not offer a blanket justification for all forms of compatriot partiality. Partiality between members of oppressed groups is only a temporary effective measure designed to level an unlevel playing field. Second, because history attests that sovereign republics could arise as a collective response to colonial oppression, justifying compatriot partiality on the grounds that I have identified is conducive to the development of sovereignty and even democracy in poor countries, thereby avoiding problems of infringement that many humanitarian poverty alleviation efforts encounter. Finally, my justification for compatriot partiality complies with the implicit cosmopolitan commitment to the realizability of global justice

  17. A stochastic cloud model for cloud and ozone retrievals from UV measurements

    International Nuclear Information System (INIS)

    Efremenko, Dmitry S.; Schüssler, Olena; Doicu, Adrian; Loyola, Diego

    2016-01-01

    The new generation of satellite instruments provides measurements in and around the Oxygen A-band on a global basis and with a relatively high spatial resolution. These data are commonly used for the determination of cloud properties. A stochastic model and radiative transfer model, previously developed by the authors, is used as the forward model component in retrievals of cloud parameters and ozone total and partial columns. The cloud retrieval algorithm combines local and global optimization routines, and yields a retrieval accuracy of about 1% and a fast computational time. Retrieved parameters are the cloud optical thickness and the cloud-top height. It was found that the use of the independent pixel approximation instead of the stochastic cloud model leads to large errors in the retrieved cloud parameters, as well as, in the retrieved ozone height resolved partial columns. The latter can be reduced by using the stochastic cloud model to compute the optimal value of the regularization parameter in the framework of Tikhonov regularization. - Highlights: • A stochastic radiative transfer model for retrieving clouds/ozone is designed. • Errors of independent pixel approximation (IPA) for O3 total column are small. • The error of IPA for ozone profile retrieval may become large. • The use of stochastic model reduces the error of ozone profile retrieval.

  18. Design and Realization of Universal Data Interface

    Directory of Open Access Journals (Sweden)

    Jong-Woo Kim

    2005-03-01

    Full Text Available KARI studied data interface of Space Applications for developing Space Experimental Instrument in International Space Station, designed, and manufactured the UDIS (International Sapce Station Universal Data Interface simulator according to requirements of the data interface. This paper explains the design and implementation of UDIS for space application. UDIS is the instrument which simulate to interface the data from ISS to experiment module, payload and habitation module and use the development of a experiment system in the space. This simulator will be used to the GSE (Ground Support Equipment for test of experiment system. By realization of the simulator, we ensure data interface skills for a manned-space data communication system.

  19. Effective Complexity of Stationary Process Realizations

    Directory of Open Access Journals (Sweden)

    Arleta Szkoła

    2011-06-01

    Full Text Available The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, which is the probability distributions on finite binary strings. In our previous paper [1] we propose a definition of effective complexity in precise terms of algorithmic information theory. Here we investigate the effective complexity of binary strings generated by stationary, in general not computable, processes. We show that under not too strong conditions long typical process realizations are effectively simple. Our results become most transparent in the context of coarse effective complexity which is a modification of the original notion of effective complexity that needs less parameters in its definition. A similar modification of the related concept of sophistication has been suggested by Antunes and Fortnow.

  20. Realized Variance and Market Microstructure Noise

    DEFF Research Database (Denmark)

    Hansen, Peter R.; Lunde, Asger

    2006-01-01

    We study market microstructure noise in high-frequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel......-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Industrial Average stocks reveals that market microstructure noise its time-dependent and correlated with increments in the efficient price. This has important implications for volatility...... estimation based on high-frequency data. Finally, we apply cointegration techniques to decompose transaction prices and bid-ask quotes into an estimate of the efficient price and noise. This framework enables us to study the dynamic effects on transaction prices and quotes caused by changes in the efficient...

  1. Challenges in realizing ultraflat materials surfaces

    Directory of Open Access Journals (Sweden)

    Takashi Yatsui

    2013-12-01

    Full Text Available Ultraflat surface substrates are required to achieve an optimal performance of future optical, electronic, or optoelectronic devices for various applications, because such surfaces reduce the scattering loss of photons, electrons, or both at the surfaces and interfaces. In this paper, we review recent progress toward the realization of ultraflat materials surfaces. First, we review the development of surface-flattening techniques. Second, we briefly review the dressed photon–phonon (DPP, a nanometric quasiparticle that describes the coupled state of a photon, an electron, and a multimode-coherent phonon. Then, we review several recent developments based on DPP-photochemical etching and desorption processes, which have resulted in angstrom-scale flat surfaces. To confirm that the superior flatness of these surfaces that originated from the DPP process, we also review a simplified mathematical model that describes the scale-dependent effects of optical near-fields. Finally, we present the future outlook for these technologies.

  2. Design and Realization of Intelligent Flow Controller

    Directory of Open Access Journals (Sweden)

    Jianxiong Ye

    2014-09-01

    Full Text Available According to accurate flow rate control requirements in large irrigation zone, a fuzzy controller with dead-band is designed on the characteristics analysis and comparison of PID and Fuzzy. The setting values of water flow for gates are determined by real-time water level detection sensors, and the realistic value of discharged water and gate opening are detected out with relative sensors, simulation manifest that the specific control strategy can adjust the gate swiftly in circumstance of huge offset, and regulate the gate slightly in time of small bias, it is realized with Siemens S315 PLC (Programmable Logical Controller and has being working steadily for 2 years, the aim of regulation is performed properly.

  3. Realization of mechanical rotation in superfluid helium

    Science.gov (United States)

    Gordon, E. B.; Kulish, M. I.; Karabulin, A. V.; Matyushenko, V. I.; Dyatlova, E. V.; Gordienko, A. S.; Stepanov, M. E.

    2017-09-01

    The possibility of using miniaturized low-power electric motors submerged in superfluid helium for organization of rotation inside a cryostat has been investigated. It has been revealed that many of commercial micromotors can operate in liquid helium consuming low power. Turret with 5 sample holders, assembled on the base of stepper motor, has been successfully tested in experiments on the nanowire production in quantized vortices of superfluid helium. Application of the stepper motor made it possible in a single experiment to study the effect of various experimental parameters on the yield and quality of the nanowires. The promises for continuous fast rotation of the bath filled by superfluid helium by using high-speed brushless micromotor were outlined and tested. Being realized, this approach will open new possibility to study the guest particles interaction with the array of parallel linear vortices in He II.

  4. Stochastic modeling of pitting corrosion: A new model for initiation and growth of multiple corrosion pits

    International Nuclear Information System (INIS)

    Valor, A.; Caleyo, F.; Alfonso, L.; Rivas, D.; Hallen, J.M.

    2007-01-01

    In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion

  5. Stochastic modeling of pitting corrosion: A new model for initiation and growth of multiple corrosion pits

    Energy Technology Data Exchange (ETDEWEB)

    Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 Havana (Cuba); Caleyo, F. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)]. E-mail: fcaleyo@gmail.com; Alfonso, L. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Rivas, D. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Hallen, J.M. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)

    2007-02-15

    In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion.

  6. A constrained approach to multiscale stochastic simulation of chemically reacting systems

    KAUST Repository

    Cotter, Simon L.

    2011-01-01

    Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. © 2011 American Institute of Physics.

  7. Digital hardware implementation of a stochastic two-dimensional neuron model.

    Science.gov (United States)

    Grassia, F; Kohno, T; Levi, T

    2016-11-01

    This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments. Copyright © 2017 Elsevier Ltd. All rights reserved.

  8. A stochastic multiscale framework for modeling flow through random heterogeneous porous media

    International Nuclear Information System (INIS)

    Ganapathysubramanian, B.; Zabaras, N.

    2009-01-01

    Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given

  9. Chaotic transitions in deterministic and stochastic dynamical systems applications of Melnikov processes in engineering, physics, and neuroscience

    CERN Document Server

    Simiu, Emil

    2002-01-01

    The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to d...

  10. Pricing real estate index options under stochastic interest rates

    Science.gov (United States)

    Gong, Pu; Dai, Jun

    2017-08-01

    Real estate derivatives as new financial instruments are not merely risk management tools but also provide a novel way to gain exposure to real estate assets without buying or selling the physical assets. Although real estate derivatives market has exhibited a rapid development in recent years, the valuation challenge of real estate derivatives remains a great obstacle for further development in this market. In this paper, we derive a partial differential equation contingent on a real estate index in a stochastic interest rate environment and propose a modified finite difference method that adopts the non-uniform grids to solve this problem. Numerical results confirm the efficiency of the method and indicate that constant interest rate models lead to the mispricing of options and the effects of stochastic interest rates on option prices depend on whether the term structure of interest rates is rising or falling. Finally, we have investigated and compared the different effects of stochastic interest rates on European and American option prices.

  11. Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

    International Nuclear Information System (INIS)

    Goreac, D.

    2009-01-01

    The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case

  12. Global sensitivity analysis in stochastic simulators of uncertain reaction networks.

    Science.gov (United States)

    Navarro Jimenez, M; Le Maître, O P; Knio, O M

    2016-12-28

    Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

  13. A stochastic solution of the advective transport equation with uncertainty

    International Nuclear Information System (INIS)

    Williams, M.M.R.

    1991-01-01

    A model has been developed for calculating the transport of water-borne radionuclides through layers of porous materials, such as rock or clay. The model is based upon a purely advective transport equation, in which the fluid velocity is a random variable, thereby simulating dispersion in a more realistic manner than the ad hoc introduction of a dispersivity. In addition to a random velocity field, which is an observable physical phenomenon, allowance is made for uncertainty in our knowledge of the parameters which enter the equation, e.g. the retardation coefficient. This too, is assumed to be a random variable and contributes to the stochasticity of the resulting partial differential equation of transport. The stochastic differential equation can be solved analytically and then ensemble averages taken over the associated probability distribution of velocity and retardation coefficient. A method based upon a novel form of the central limit theorem of statistics is employed to obtain tractable solutions of a system consisting of many serial legs of varying properties. One interesting conclusion is that the total flux out of a medium is significantly underestimated by using the deterministic solution with an average transit time compared with that from the stochastically averaged solution. The theory is illustrated numerically for a number of physically relevant cases. (author) 8 figs., 4 tabs., 7 refs

  14. Global sensitivity analysis in stochastic simulators of uncertain reaction networks

    KAUST Repository

    Navarro, María

    2016-12-26

    Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

  15. Verification of Stochastic Process Calculi

    DEFF Research Database (Denmark)

    Skrypnyuk, Nataliya

    algorithms for constructing bisimulation relations, computing (overapproximations of) sets of reachable states and computing the expected time reachability, the last for a linear fragment of IMC. In all the cases we have the complexities of algorithms which are low polynomial in the size of the syntactic....... In support of this claim we have developed analysis methods that belong to a particular type of Static Analysis { Data Flow / Pathway Analysis. These methods have previously been applied to a number of non-stochastic process calculi. In this thesis we are lifting them to the stochastic calculus...... of Interactive Markov Chains (IMC). We have devised the Pathway Analysis of IMC that is not only correct in the sense of overapproximating all possible behaviour scenarios, as is usual for Static Analysis methods, but is also precise. This gives us the possibility to explicitly decide on the trade-o between...

  16. Fourier analysis and stochastic processes

    CERN Document Server

    Brémaud, Pierre

    2014-01-01

    This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...

  17. Stochastic integration and differential equations

    CERN Document Server

    Protter, Philip E

    2003-01-01

    It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...

  18. The dynamics of stochastic processes

    DEFF Research Database (Denmark)

    Basse-O'Connor, Andreas

    In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... to the Bichteler-Dellacherie Theorem. The semimartingale property of Gaussian processes is characterized in terms of their covariance function, spectral measure and spectral representation. In addition, representation and expansion of filtration results are provided as well. Special attention is given to moving...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...

  19. Modular invariance and stochastic quantization

    International Nuclear Information System (INIS)

    Ordonez, C.R.; Rubin, M.A.; Zwanziger, D.

    1989-01-01

    In Polyakov path integrals and covariant closed-string field theory, integration over Teichmueller parameters must be restricted by hand to a single modular region. This problem has an analog in Yang-Mills gauge theory---namely, the Gribov problem, which can be resolved by the method of stochastic gauge fixing. This method is here employed to quantize a simple modular-invariant system: the Polyakov point particle. In the limit of a large gauge-fixing force, it is shown that suitable choices for the functional form of the gauge-fixing force can lead to a restriction of Teichmueller integration to a single modular region. Modifications which arise when applying stochastic quantization to a system in which the volume of the orbits of the gauge group depends on a dynamical variable, such as a Teichmueller parameter, are pointed out, and the extension to Polyakov strings and covariant closed-string field theory is discussed

  20. Stochastic models for atmospheric dispersion

    DEFF Research Database (Denmark)

    Ditlevsen, Ove Dalager

    2003-01-01

    Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...

  1. Stochastic Generalized Method of Moments

    KAUST Repository

    Yin, Guosheng; Ma, Yanyuan; Liang, Faming; Yuan, Ying

    2011-01-01

    The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.

  2. Stochastic problems in population genetics

    CERN Document Server

    Maruyama, Takeo

    1977-01-01

    These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura...

  3. Stochastic Generalized Method of Moments

    KAUST Repository

    Yin, Guosheng

    2011-08-16

    The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.

  4. Limits for Stochastic Reaction Networks

    DEFF Research Database (Denmark)

    Cappelletti, Daniele

    Reaction systems have been introduced in the 70s to model biochemical systems. Nowadays their range of applications has increased and they are fruitfully used in dierent elds. The concept is simple: some chemical species react, the set of chemical reactions form a graph and a rate function...... is associated with each reaction. Such functions describe the speed of the dierent reactions, or their propensities. Two modelling regimes are then available: the evolution of the dierent species concentrations can be deterministically modelled through a system of ODE, while the counts of the dierent species...... at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...

  5. Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm

    International Nuclear Information System (INIS)

    Takaishi, Tetsuya

    2013-01-01

    The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.

  6. Some Topics in Stochastic Control

    Science.gov (United States)

    2010-10-14

    assimilation problems. (a) Papers published in peer-reviewed journals (N/A for none) 1. R. Atar and A. Budhiraja. A stochastic differential game for...the inhomogeneous infinity-Laplace equation. Ann. Prob., 38 (2010), no. 2, 498--531. 2. R. Atar and A. Budhiraja. On near optimal trajectories for a...G. Aronsson. A mathematical model in sand mechanics: presentation and analysis. SIAM J. Appl. Math., 22 (1972), 437-458 [3] R. Atar and A. Budhiraja

  7. Stochastic background of atmospheric cascades

    International Nuclear Information System (INIS)

    Wilk, G.; Wlodarczyk, Z.

    1993-01-01

    Fluctuations in the atmospheric cascades developing during the propagation of very high energy cosmic rays through the atmosphere are investigated using stochastic branching model of pure birth process with immigration. In particular, we show that the multiplicity distributions of secondaries emerging from gamma families are much narrower than those resulting from hadronic families. We argue that the strong intermittent like behaviour found recently in atmospheric families results from the fluctuations in the cascades themselves and are insensitive to the details of elementary interactions

  8. Foundations of infinitesimal stochastic analysis

    CERN Document Server

    Stroyan, KD

    2011-01-01

    This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

  9. Optimal Advertising with Stochastic Demand

    OpenAIRE

    George E. Monahan

    1983-01-01

    A stochastic, sequential model is developed to determine optimal advertising expenditures as a function of product maturity and past advertising. Random demand for the product depends upon an aggregate measure of current and past advertising called "goodwill," and the position of the product in its life cycle measured by sales-to-date. Conditions on the parameters of the model are established that insure that it is optimal to advertise less as the product matures. Additional characteristics o...

  10. Stochastic cooling technology at Fermilab

    Energy Technology Data Exchange (ETDEWEB)

    Pasquinelli, R.J. E-mail: pasquin@fnal.gov

    2004-10-11

    The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.

  11. Stochastic cooling technology at Fermilab

    Science.gov (United States)

    Pasquinelli, Ralph J.

    2004-10-01

    The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.

  12. Stochastic cooling technology at Fermilab

    International Nuclear Information System (INIS)

    Pasquinelli, R.J.

    2004-01-01

    The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented

  13. Stochastic Gravity: Theory and Applications

    Directory of Open Access Journals (Sweden)

    Hu Bei Lok

    2008-05-01

    Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out

  14. Stochastic processes and filtering theory

    CERN Document Server

    Jazwinski, Andrew H

    1970-01-01

    This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab

  15. Stochastic density functional theory at finite temperatures

    Science.gov (United States)

    Cytter, Yael; Rabani, Eran; Neuhauser, Daniel; Baer, Roi

    2018-03-01

    Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O Stochastic processes, slaves and supersymmetry

    International Nuclear Information System (INIS)

    Drummond, I T; Horgan, R R

    2012-01-01

    We extend the work of Tănase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the stochastic differential equations (SDEs) for the process and the associated diffusion equation. The influence of the disturbances can be understood by augmenting the original SDE with an equation for slave variables. The evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow. These line elements, together with the associated surface and volume elements constructed from them, provide the basis of the supersymmetry properties of the theory. For ease of visualization, and in order to emphasize a helpful electromagnetic analogy, we work in three dimensions. The results are all generalizable to higher dimensions and can be specialized to one and two dimensions. The electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations. We also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations. We pay special attention to the dependence of the slave variable statistics on temperature. We identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities. (paper)

  16. Stochastic cooling in muon colliders

    International Nuclear Information System (INIS)

    Barletta, W.A.; Sessler, A.M.

    1993-09-01

    Analysis of muon production techniques for high energy colliders indicates the need for rapid and effective beam cooling in order that one achieve luminosities > 10 30 cm -2 s -1 as required for high energy physics experiments. This paper considers stochastic cooling to increase the phase space density of the muons in the collider. Even at muon energies greater than 100 GeV, the number of muons per bunch must be limited to ∼10 3 for the cooling rate to be less than the muon lifetime. With such a small number of muons per bunch, the final beam emittance implied by the luminosity requirement is well below the thermodynamic limit for beam electronics at practical temperatures. Rapid bunch stacking after the cooling process can raise the number of muons per bunch to a level consistent with both the luminosity goals and with practical temperatures for the stochastic cooling electronics. A major advantage of our stochastic cooling/stacking scheme over scenarios that employ only ionization cooling is that the power on the production target can be reduced below 1 MW

  17. Stochastic analysis of biochemical systems

    CERN Document Server

    Anderson, David F

    2015-01-01

    This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology.  The book should serve well as a supplement for courses in probability and stochastic processes.  While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest.    David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...

  18. Stochastic inflation and nonlinear gravity

    International Nuclear Information System (INIS)

    Salopek, D.S.; Bond, J.R.

    1991-01-01

    We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is T=ln(Ha), where H and a are the local values of the Hubble parameter and the scale factor, since T is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background

  19. Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Application

    KAUST Repository

    Chambolle, Antonin; Ehrhardt, Matthias J.; Richtarik, Peter; Schö nlieb, Carola-Bibiane

    2017-01-01

    We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.