Estimating the parameters of stochastic differential equations using a criterion function based on the Kolmogorov-Smirnov statistic

OpenAIRE

McDonald, A. David; Sandal, Leif Kristoffer

1998-01-01

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per replication. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic, put forward by Hurn and Lin...

Stability of numerical method for semi-linear stochastic pantograph differential equations

Directory of Open Access Journals (Sweden)

Yu Zhang

2016-01-01

Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

Stochastic calculus analysis of optical time-of-flight range imaging and estimation of radial motion.

Science.gov (United States)

Streeter, Lee

2017-07-01

Time-of-flight range imaging is analyzed using stochastic calculus. Through a series of interpretations and simplifications, the stochastic model leads to two methods for estimating linear radial velocity: maximum likelihood estimation on the transition probability distribution between measurements, and a new method based on analyzing the measured correlation waveform and its first derivative. The methods are tested in a simulated motion experiment from (-40)-(+40)  m/s, with data from a camera imaging an object on a translation stage. In tests maximum likelihood is slow and unreliable, but when it works it estimates the linear velocity with standard deviation of 1 m/s or better. In comparison the new method is fast and reliable but works in a reduced velocity range of (-20)-(+20)  m/s with standard deviation ranging from 3.5 m/s to 10 m/s.

Development of stochastic webs in a wave-driven linear oscillator

International Nuclear Information System (INIS)

Murakami, Sadayoshi; Sato, Tetsuya; Hasegawa, Akira.

1988-01-01

We present developments of stochastic webs in a linear oscillator which is driven by a finite number (N) of external waves with frequency ω o (harmonic of the linear oscillator frequency). The expansion of the stochastic domain as functions of the number of waves and their amplitudes is studied numerically. The results with small amplitude waves compares well with the perturbation theory. When the amplitude of external waves is small a leaf structure which expands with N develops radially in the phase space. (author)

Nelson's stochastic quantization of free linearized gravitational field and its Markovian structure

International Nuclear Information System (INIS)

Lim, S.C.

1983-05-01

It is shown that by applying Nelson's stochastic quantization scheme to free linearized gravitational field tensor one can associate with the resulting stochastic system a stochastic tensor field which coincides with the ''space'' part of the Riemannian tensor in Euclidean space-time. However, such a stochastic field fails to satisfy the Markov property. Instead, it satisfies the reflection positivity. The Markovian structure of the stochastic fields associated with the electromagnetic field is also discussed. (author)

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

Science.gov (United States)

Li, Pu; Chen, Bing

2011-04-01

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

Stochastic equivalent linearization in 3-D hysteretic frames

International Nuclear Information System (INIS)

Casciati, F.; Faravelli, L.

1987-01-01

Stochastic equivalent linearization technique for hysteretic systems is extended to study the dynamic response of 3-D frames with hysteretic constitutive laws in the potential plastic hinges. The constitutive law is idealized by an appropriate endochronic model. A general purpose finite element code is adopted in order to generate the matrices by which the equations of motion to be linearized are built. (orig./HP)

State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.

Science.gov (United States)

1978-12-01

The state estimation problem of linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered, especially the case...where the incident intensities of the Poisson processes are low and the system is observed in an additive white Gaussian noise. The minimum mean squared

Linear stochastic differential equations with anticipating initial conditions

DEFF Research Database (Denmark)

Khalifa, Narjess; Kuo, Hui-Hsiung; Ouerdiane, Habib

In this paper we use the new stochastic integral introduced by Ayed and Kuo (2008) and the results obtained by Kuo et al. (2012b) to find a solution to a drift-free linear stochastic differential equation with anticipating initial condition. Our solution is based on well-known results from...... classical Itô theory and anticipative Itô formula results from Kue et al. (2012b). We also show that the solution obtained by our method is consistent with the solution obtained by the methods of Malliavin calculus, e.g. Buckdahn and Nualart (1994)....

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...

Estimation of Stochastic Volatility Models by Nonparametric Filtering

DEFF Research Database (Denmark)

Kanaya, Shin; Kristensen, Dennis

2016-01-01

/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases...... and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties...

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)

Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

Science.gov (United States)

Frank, T D; Beek, P J

2001-08-01

Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Science.gov (United States)

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

Comparison of deterministic and stochastic techniques for estimation of design basis floods for nuclear power plants

International Nuclear Information System (INIS)

Solomon, S.I.; Harvey, K.D.

1982-12-01

The IAEA Safety Guide 50-SG-S10A recommends that design basis floods be estimated by deterministic techniques using probable maximum precipitation and a rainfall runoff model to evaluate the corresponding flood. The Guide indicates that stochastic techniques are also acceptable in which case floods of very low probability have to be estimated. The paper compares the results of applying the two techniques in two river basins at a number of locations and concludes that the uncertainty of the results of both techniques is of the same order of magnitude. However, the use of the unit hydrograph as the rainfall runoff model may lead in some cases to nonconservative estimates. A distributed non-linear rainfall runoff model leads to estimates of probable maximum flood flows which are very close to values of flows having a 10 6 - 10 7 years return interval estimated using a conservative and relatively simple stochastic technique. Recommendations on the practical application of Safety Guide 50-SG-10A are made and the extension of the stochastic technique to ungauged sites and other design parameters is discussed

Gradient-based stochastic estimation of the density matrix

Science.gov (United States)

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

2018-03-01

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

Slope Estimation in Noisy Piecewise Linear Functions.

Science.gov (United States)

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2015-03-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure.

Comparison of deterministic and stochastic techniques for estimation of design basis floods for nuclear power plants

International Nuclear Information System (INIS)

Solomon, S.I.; Harvey, K.D.; Asmis, G.J.K.

1983-01-01

The IAEA Safety Guide 50-SG-S10A recommends that design basis floods be estimated by deterministic techniques using probable maximum precipitation and a rainfall runoff model to evaluate the corresponding flood. The Guide indicates that stochastic techniques are also acceptable in which case floods of very low probability have to be estimated. The paper compares the results of applying the two techniques in two river basins at a number of locations and concludes that the uncertainty of the results of both techniques is of the same order of magnitude. However, the use of the unit hydrograph as the rain fall runoff model may lead in some cases to non-conservative estimates. A distributed non-linear rainfall runoff model leads to estimates of probable maximum flood flows which are very close to values of flows having a 10 6 to 10 7 years return interval estimated using a conservative and relatively simple stochastic technique. Recommendations on the practical application of Safety Guide 50-SG-10A are made and the extension of the stochastic technique to ungauged sites and other design parameters is discussed

Estimation of error components in a multi-error linear regression model, with an application to track fitting

International Nuclear Information System (INIS)

Fruehwirth, R.

1993-01-01

We present an estimation procedure of the error components in a linear regression model with multiple independent stochastic error contributions. After solving the general problem we apply the results to the estimation of the actual trajectory in track fitting with multiple scattering. (orig.)

Parameter estimation in stochastic rainfall-runoff models

DEFF Research Database (Denmark)

Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur

2006-01-01

A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...

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.

A Non-linear Stochastic Model for an Office Building with Air Infiltration

DEFF Research Database (Denmark)

Thavlov, Anders; Madsen, Henrik

2015-01-01

This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...

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.

Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

International Nuclear Information System (INIS)

Grigoriu, Mircea; Samorodnitsky, Gennady

2004-01-01

Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

Science.gov (United States)

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

Energy Technology Data Exchange (ETDEWEB)

Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)

2014-06-19

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Fast and robust estimation of spectro-temporal receptive fields using stochastic approximations.

Science.gov (United States)

Meyer, Arne F; Diepenbrock, Jan-Philipp; Ohl, Frank W; Anemüller, Jörn

2015-05-15

The receptive field (RF) represents the signal preferences of sensory neurons and is the primary analysis method for understanding sensory coding. While it is essential to estimate a neuron's RF, finding numerical solutions to increasingly complex RF models can become computationally intensive, in particular for high-dimensional stimuli or when many neurons are involved. Here we propose an optimization scheme based on stochastic approximations that facilitate this task. The basic idea is to derive solutions on a random subset rather than computing the full solution on the available data set. To test this, we applied different optimization schemes based on stochastic gradient descent (SGD) to both the generalized linear model (GLM) and a recently developed classification-based RF estimation approach. Using simulated and recorded responses, we demonstrate that RF parameter optimization based on state-of-the-art SGD algorithms produces robust estimates of the spectro-temporal receptive field (STRF). Results on recordings from the auditory midbrain demonstrate that stochastic approximations preserve both predictive power and tuning properties of STRFs. A correlation of 0.93 with the STRF derived from the full solution may be obtained in less than 10% of the full solution's estimation time. We also present an on-line algorithm that allows simultaneous monitoring of STRF properties of more than 30 neurons on a single computer. The proposed approach may not only prove helpful for large-scale recordings but also provides a more comprehensive characterization of neural tuning in experiments than standard tuning curves. Copyright © 2015 Elsevier B.V. All rights reserved.

Stochastic quantum inflation for a canonical scalar field with linear self-interaction potential

Energy Technology Data Exchange (ETDEWEB)

Panotopoulos, Grigoris [CENTRA, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa (Portugal)

2017-10-15

We apply Starobinsky's formalism of stochastic inflation to the case of a massless minimally coupled scalar field with linear self-interaction potential. We solve the corresponding Fokker-Planck equation exactly, and we obtain analytical expressions for the stochastic expectation values. (orig.)

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

Efficient Estimating Functions for Stochastic Differential Equations

DEFF Research Database (Denmark)

Jakobsen, Nina Munkholt

The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...

Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models

Science.gov (United States)

Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.

2018-02-01

In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.

Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics

DEFF Research Database (Denmark)

Iwankiewicz, R.; Nielsen, Søren R. K.

Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...

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.

Linearly convergent stochastic heavy ball method for minimizing generalization error

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss

Alternative Approaches to Technical Efficiency Estimation in the Stochastic Frontier Model

OpenAIRE

Acquah, H. de-Graft; Onumah, E. E.

2014-01-01

Estimating the stochastic frontier model and calculating technical efficiency of decision making units are of great importance in applied production economic works. This paper estimates technical efficiency from the stochastic frontier model using Jondrow, and Battese and Coelli approaches. In order to compare alternative methods, simulated data with sample sizes of 60 and 200 are generated from stochastic frontier model commonly applied to agricultural firms. Simulated data is employed to co...

Bias-reduced estimation of long memory stochastic volatility

DEFF Research Database (Denmark)

Frederiksen, Per; Nielsen, Morten Ørregaard

We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstation- arity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining...

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

Science.gov (United States)

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience

Directory of Open Access Journals (Sweden)

Yan Chen

2017-01-01

Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.

Stochastic development regression using method of moments

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

This paper considers the estimation problem arising when inferring parameters in the stochastic development regression model for manifold valued non-linear data. Stochastic development regression captures the relation between manifold-valued response and Euclidean covariate variables using...... the stochastic development construction. It is thereby able to incorporate several covariate variables and random effects. The model is intrinsically defined using the connection of the manifold, and the use of stochastic development avoids linearizing the geometry. We propose to infer parameters using...... the Method of Moments procedure that matches known constraints on moments of the observations conditional on the latent variables. The performance of the model is investigated in a simulation example using data on finite dimensional landmark manifolds....

Using linear programming to analyze and optimize stochastic flow lines

DEFF Research Database (Denmark)

Helber, Stefan; Schimmelpfeng, Katja; Stolletz, Raik

2011-01-01

This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time...... programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines....

Efficient AM Algorithms for Stochastic ML Estimation of DOA

Directory of Open Access Journals (Sweden)

Haihua Chen

2016-01-01

Full Text Available The estimation of direction-of-arrival (DOA of signals is a basic and important problem in sensor array signal processing. To solve this problem, many algorithms have been proposed, among which the Stochastic Maximum Likelihood (SML is one of the most concerned algorithms because of its high accuracy of DOA. However, the estimation of SML generally involves the multidimensional nonlinear optimization problem. As a result, its computational complexity is rather high. This paper addresses the issue of reducing computational complexity of SML estimation of DOA based on the Alternating Minimization (AM algorithm. We have the following two contributions. First using transformation of matrix and properties of spatial projection, we propose an efficient AM (EAM algorithm by dividing the SML criterion into two components. One depends on a single variable parameter while the other does not. Second when the array is a uniform linear array, we get the irreducible form of the EAM criterion (IAM using polynomial forms. Simulation results show that both EAM and IAM can reduce the computational complexity of SML estimation greatly, while IAM is the best. Another advantage of IAM is that this algorithm can avoid the numerical instability problem which may happen in AM and EAM algorithms when more than one parameter converges to an identical value.

Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters

Directory of Open Access Journals (Sweden)

Wen Xu

2016-10-01

Full Text Available Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackwellized particle filters. Monte Carlo studies reveal the good and stable performance of our particle filter-based estimator. When the volatility of volatility is high, or when regressors are absent but stochastic volatility exists, our approach can be better than the maximum likelihood estimator which neglects stochastic volatility and generalized method of moments (GMM estimators.

Estimating Stochastic Volatility Models using Prediction-based Estimating Functions

DEFF Research Database (Denmark)

Lunde, Asger; Brix, Anne Floor

to the performance of the GMM estimator based on conditional moments of integrated volatility from Bollerslev and Zhou (2002). The case where the observed log-price process is contaminated by i.i.d. market microstructure (MMS) noise is also investigated. First, the impact of MMS noise on the parameter estimates from......In this paper prediction-based estimating functions (PBEFs), introduced in Sørensen (2000), are reviewed and PBEFs for the Heston (1993) stochastic volatility model are derived. The finite sample performance of the PBEF based estimator is investigated in a Monte Carlo study, and compared...... to correctly account for the noise are investigated. Our Monte Carlo study shows that the estimator based on PBEFs outperforms the GMM estimator, both in the setting with and without MMS noise. Finally, an empirical application investigates the possible challenges and general performance of applying the PBEF...

On estimation of stochastic forcing with application to El Niño

Science.gov (United States)

Penland, C.

2014-12-01

Although Linear Inverse Modeling (LIM) provides skillful forecasts of tropical ocean sea surface temperatures, LIM's diagnostic properties are at least as useful as its prognostic properties. In this presentation, we discuss an updated method for using LIM to obtain time series representing stochastic forcing of El Niño and to quantify particular unpredictable contributions to LIM forecast error. Attention is paid to the proper stochastic calculus and to the time scale separation between the stochastic forcing and El Niño's signal. The method yields seldom-considered sources of El Niño's stochastic forcing.

Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

Directory of Open Access Journals (Sweden)

Peng Fangfang

2014-01-01

Full Text Available This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

Energy Technology Data Exchange (ETDEWEB)

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

A computer model of the biosphere, to estimate stochastic and non-stochastic effects of radionuclides on humans

International Nuclear Information System (INIS)

Laurens, J.M.

1985-01-01

A computer code was written to model food chains in order to estimate the internal and external doses, for stochastic and non-stochastic effects, on humans (adults and infants). Results are given for 67 radionuclides, for unit concentration in water (1 Bq/L) and in atmosphere (1 Bq/m 3 )

Some Additional Remarks on the Cumulant Expansion for Linear Stochastic Differential Equations

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1984-01-01

We summarize our previous results on cumulant expansions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

Some additional remarks on the cumulant expansion for linear stochastic differential equations

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1984-01-01

We summarize our previous results on cumular expasions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

Simple Planar Truss (Linear, Nonlinear and Stochastic Approach

Directory of Open Access Journals (Sweden)

Frydrýšek Karel

2016-11-01

Full Text Available This article deals with a simple planar and statically determinate pin-connected truss. It demonstrates the processes and methods of derivations and solutions according to 1st and 2nd order theories. The article applies linear and nonlinear approaches and their simplifications via a Maclaurin series. Programming connected with the stochastic Simulation-Based Reliability Method (i.e. the direct Monte Carlo approach is used to conduct a probabilistic reliability assessment (i.e. a calculation of the probability that plastic deformation will occur in members of the truss.

Asymptotic analysis of a stochastic non-linear nuclear reactor model

International Nuclear Information System (INIS)

Rodriguez, M.A.; Sancho, J.M.

1986-01-01

The asymptotic behaviour of a stochastic non-linear nuclear reactor modelled by a master equation is analysed in two different limits: the thermodynamic limit and the zero-neutron-source limit. In the first limit a finite steady neutron density is obtained. The second limit predicts the neutron extinction. The interplay between these two limits is studied for different situations. (author)

Stability Criterion of Linear Stochastic Systems Subject to Mixed H2/Passivity Performance

Directory of Open Access Journals (Sweden)

Cheung-Chieh Ku

2015-01-01

Full Text Available The H2 control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, the H2 control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.

Estimation of Nonlinear Functions of State Vector for Linear Systems with Time-Delays and Uncertainties

Directory of Open Access Journals (Sweden)

Il Young Song

2015-01-01

Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.

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)

A new unbiased stochastic derivative estimator for discontinuous sample performances with structural parameters

NARCIS (Netherlands)

Peng, Yijie; Fu, Michael C.; Hu, Jian Qiang; Heidergott, Bernd

In this paper, we propose a new unbiased stochastic derivative estimator in a framework that can handle discontinuous sample performances with structural parameters. This work extends the three most popular unbiased stochastic derivative estimators: (1) infinitesimal perturbation analysis (IPA), (2)

Test models for improving filtering with model errors through stochastic parameter estimation

International Nuclear Information System (INIS)

Gershgorin, B.; Harlim, J.; Majda, A.J.

2010-01-01

The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

CERN Document Server

Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

2017-01-01

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

Role of statistical linearization in the solution of nonlinear stochastic equations

International Nuclear Information System (INIS)

Budgor, A.B.

1977-01-01

The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables

Periodic linear differential stochastic processes

NARCIS (Netherlands)

Kwakernaak, H.

1975-01-01

Periodic linear differential processes are defined and their properties are analyzed. Equivalent representations are discussed, and the solutions of related optimal estimation problems are given. An extension is presented of Kailath and Geesey’s [1] results concerning the innovations representation

Efficient decomposition and linearization methods for the stochastic transportation problem

International Nuclear Information System (INIS)

Holmberg, K.

1993-01-01

The stochastic transportation problem can be formulated as a convex transportation problem with nonlinear objective function and linear constraints. We compare several different methods based on decomposition techniques and linearization techniques for this problem, trying to find the most efficient method or combination of methods. We discuss and test a separable programming approach, the Frank-Wolfe method with and without modifications, the new technique of mean value cross decomposition and the more well known Lagrangian relaxation with subgradient optimization, as well as combinations of these approaches. Computational tests are presented, indicating that some new combination methods are quite efficient for large scale problems. (authors) (27 refs.)

Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

Directory of Open Access Journals (Sweden)

Daigle Bernie J

2012-05-01

Full Text Available Abstract Background A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs. MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. Results We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2: an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods

Estimation of Parameters in Mean-Reverting Stochastic Systems

Directory of Open Access Journals (Sweden)

Tianhai Tian

2014-01-01

Full Text Available Stochastic differential equation (SDE is a very important mathematical tool to describe complex systems in which noise plays an important role. SDE models have been widely used to study the dynamic properties of various nonlinear systems in biology, engineering, finance, and economics, as well as physical sciences. Since a SDE can generate unlimited numbers of trajectories, it is difficult to estimate model parameters based on experimental observations which may represent only one trajectory of the stochastic model. Although substantial research efforts have been made to develop effective methods, it is still a challenge to infer unknown parameters in SDE models from observations that may have large variations. Using an interest rate model as a test problem, in this work we use the Bayesian inference and Markov Chain Monte Carlo method to estimate unknown parameters in SDE models.

Estimation of parameter sensitivities for stochastic reaction networks

KAUST Repository

Gupta, Ankit

2016-01-07

Quantification of the effects of parameter uncertainty is an important and challenging problem in Systems Biology. We consider this problem in the context of stochastic models of biochemical reaction networks where the dynamics is described as a continuous-time Markov chain whose states represent the molecular counts of various species. For such models, effects of parameter uncertainty are often quantified by estimating the infinitesimal sensitivities of some observables with respect to model parameters. The aim of this talk is to present a holistic approach towards this problem of estimating parameter sensitivities for stochastic reaction networks. Our approach is based on a generic formula which allows us to construct efficient estimators for parameter sensitivity using simulations of the underlying model. We will discuss how novel simulation techniques, such as tau-leaping approximations, multi-level methods etc. can be easily integrated with our approach and how one can deal with stiff reaction networks where reactions span multiple time-scales. We will demonstrate the efficiency and applicability of our approach using many examples from the biological literature.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

International Nuclear Information System (INIS)

Granita; Bahar, A.

2015-01-01

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)

2015-03-09

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Model-based stochastic-deterministic State and Force Estimation using Kalman filtering with Application to Hanko-1 Channel Marker

OpenAIRE

Petersen, Øyvind Wiig

2014-01-01

Force identification in structural dynamics is an inverse problem concerned with finding loads from measured structural response. The main objective of this thesis is to perform and study state (displacement and velocity) and force estimation by Kalman filtering. Theory on optimal control and state-space models are presented, adapted to linear structural dynamics. Accommodation for measurement noise and model inaccuracies are attained by stochastic-deterministic coupling. Explicit requirem...

Linearly convergent stochastic heavy ball method for minimizing generalization error

KAUST Repository

Loizou, Nicolas

2017-10-30

In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder problem. While in the analysis we constrain ourselves to quadratic loss, the overall objective is not necessarily strongly convex.

Parameter Estimation in Stochastic Grey-Box Models

DEFF Research Database (Denmark)

Kristensen, Niels Rode; Madsen, Henrik; Jørgensen, Sten Bay

2004-01-01

An efficient and flexible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Ito stochastic differential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended...... Kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets, including irregularly sampled data sets and data sets with occasional outliers and missing observations. The software implementation is compared to an existing software tool...... and proves to have better performance both in terms of quality of estimates for nonlinear systems with significant diffusion and in terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the diffusion term....

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...

Data assimilation and uncertainty analysis of environmental assessment problems--an application of Stochastic Transfer Function and Generalised Likelihood Uncertainty Estimation techniques

International Nuclear Information System (INIS)

Romanowicz, Renata; Young, Peter C.

2003-01-01

Stochastic Transfer Function (STF) and Generalised Likelihood Uncertainty Estimation (GLUE) techniques are outlined and applied to an environmental problem concerned with marine dose assessment. The goal of both methods in this application is the estimation and prediction of the environmental variables, together with their associated probability distributions. In particular, they are used to estimate the amount of radionuclides transferred to marine biota from a given source: the British Nuclear Fuel Ltd (BNFL) repository plant in Sellafield, UK. The complexity of the processes involved, together with the large dispersion and scarcity of observations regarding radionuclide concentrations in the marine environment, require efficient data assimilation techniques. In this regard, the basic STF methods search for identifiable, linear model structures that capture the maximum amount of information contained in the data with a minimal parameterisation. They can be extended for on-line use, based on recursively updated Bayesian estimation and, although applicable to only constant or time-variable parameter (non-stationary) linear systems in the form used in this paper, they have the potential for application to non-linear systems using recently developed State Dependent Parameter (SDP) non-linear STF models. The GLUE based-methods, on the other hand, formulate the problem of estimation using a more general Bayesian approach, usually without prior statistical identification of the model structure. As a result, they are applicable to almost any linear or non-linear stochastic model, although they are much less efficient both computationally and in their use of the information contained in the observations. As expected in this particular environmental application, it is shown that the STF methods give much narrower confidence limits for the estimates due to their more efficient use of the information contained in the data. Exploiting Monte Carlo Simulation (MCS) analysis

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

Energy Technology Data Exchange (ETDEWEB)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

2017-06-15

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state

International Nuclear Information System (INIS)

Jiang, Shixiao W; Lu, Haihao; Zhou, Douglas; Cai, David

2016-01-01

Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β -Fermi–Pasta–Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems. (paper)

Fatigue damage estimation in non-linear systems using a combination of Monte Carlo simulation and the First Order Reliability Method

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2015-01-01

For non-linear systems the estimation of fatigue damage under stochastic loadings can be rather time-consuming. Usually Monte Carlo simulation (MCS) is applied, but the coefficient-of-variation (COV) can be large if only a small set of simulations can be done due to otherwise excessive CPU time...

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

Science.gov (United States)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

Empirical estimates in stochastic programs with probability and second order stochastic dominance constraints

Czech Academy of Sciences Publication Activity Database

Omelchenko, Vadym; Kaňková, Vlasta

2015-01-01

Roč. 84, č. 2 (2015), s. 267-281 ISSN 0862-9544 R&D Projects: GA ČR GA13-14445S Institutional support: RVO:67985556 Keywords : Stochastic programming problems * empirical estimates * light and heavy tailed distributions * quantiles Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2015/E/omelchenko-0454495.pdf

Economic MPC for a linear stochastic system of energy units

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura

2016-01-01

This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers...... in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...

Efficient Estimating Functions for Stochastic Differential Equations

DEFF Research Database (Denmark)

Jakobsen, Nina Munkholt

The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...... a fixed time interval. Rate optimal and effcient estimators areobtained for a one-dimensional diffusion parameter. Stable convergence in distribution isused to achieve a practically applicable Gaussian limit distribution for suitably normalisedestimators. In a simulation example, the limit distributions...... multidimensional parameter. Conditions for rate optimality and effciency of estimatorsof drift-jump and diffusion parameters are given in some special cases. Theseconditions are found to extend the pre-existing conditions applicable to continuous diffusions,and impose much stronger requirements on the estimating...

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

Science.gov (United States)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

An estimator for the relative entropy rate of path measures for stochastic differential equations

Energy Technology Data Exchange (ETDEWEB)

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

Bayesian Estimation and Inference using Stochastic Hardware

Directory of Open Access Journals (Sweden)

Chetan Singh Thakur

2016-03-01

Full Text Available In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker, demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND, we show how inference can be performed in a Directed Acyclic Graph (DAG using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

Bayesian Estimation and Inference Using Stochastic Electronics.

Science.gov (United States)

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

Stochastic modeling of mode interactions via linear parabolized stability equations

Science.gov (United States)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

DEFF Research Database (Denmark)

Sokoler, Leo Emil; Dammann, Bernd; Madsen, Henrik

2014-01-01

This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP...

Estimation of local concentration from measurements of stochastic adsorption dynamics using carbon nanotube-based sensors

International Nuclear Information System (INIS)

Jang, Hong; Lee, Jay H.; Braatz, Richard D.

2016-01-01

This paper proposes a maximum likelihood estimation (MLE) method for estimating time varying local concentration of the target molecule proximate to the sensor from the time profile of monomolecular adsorption and desorption on the surface of the sensor at nanoscale. Recently, several carbon nanotube sensors have been developed that can selectively detect target molecules at a trace concentration level. These sensors use light intensity changes mediated by adsorption or desorption phenomena on their surfaces. The molecular events occurring at trace concentration levels are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), composed of a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the significant stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should lead to an improved accuracy over than deterministic estimation formulated based on the continuum model. Motivated by this expectation, we formulate the MLE based on an analytical solution of the relevant CME, both for the constant and the time-varying local concentrations, with the objective of estimating the analyte concentration field in real time from the adsorption readings of the sensor array. The performances of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process. Some future challenges are described for estimating and controlling the concentration field in a distributed domain using the sensor technology.

Parameter estimation in a simple stochastic differential equation for phytoplankton modelling

DEFF Research Database (Denmark)

Møller, Jan Kloppenborg; Madsen, Henrik; Carstensen, Jacob

2011-01-01

The use of stochastic differential equations (SDEs) for simulation of aquatic ecosystems has attracted increasing attention in recent years. The SDE setting also provides the opportunity for statistical estimation of ecosystem parameters. We present an estimation procedure, based on Kalman...

Bayesian parameter estimation for stochastic models of biological cell migration

Science.gov (United States)

Dieterich, Peter; Preuss, Roland

2013-08-01

Cell migration plays an essential role under many physiological and patho-physiological conditions. It is of major importance during embryonic development and wound healing. In contrast, it also generates negative effects during inflammation processes, the transmigration of tumors or the formation of metastases. Thus, a reliable quantification and characterization of cell paths could give insight into the dynamics of these processes. Typically stochastic models are applied where parameters are extracted by fitting models to the so-called mean square displacement of the observed cell group. We show that this approach has several disadvantages and problems. Therefore, we propose a simple procedure directly relying on the positions of the cell's trajectory and the covariance matrix of the positions. It is shown that the covariance is identical with the spatial aging correlation function for the supposed linear Gaussian models of Brownian motion with drift and fractional Brownian motion. The technique is applied and illustrated with simulated data showing a reliable parameter estimation from single cell paths.

Evapotranspiration Estimates for a Stochastic Soil-Moisture Model

Science.gov (United States)

Chaleeraktrakoon, Chavalit; Somsakun, Somrit

2009-03-01

Potential evapotranspiration is information that is necessary for applying a widely used stochastic model of soil moisture (I. Rodriguez Iturbe, A. Porporato, L. Ridolfi, V. Isham and D. R. Cox, Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation, Proc. Roy. Soc. London A455 (1999) 3789-3805). An objective of the present paper is thus to find a proper estimate of the evapotranspiration for the stochastic model. This estimate is obtained by comparing the calculated soil-moisture distribution resulting from various techniques, such as Thornthwaite, Makkink, Jensen-Haise, FAO Modified Penman, and Blaney-Criddle, with an observed one. The comparison results using five sequences of daily soil-moisture for a dry season from November 2003 to April 2004 (Udornthani Province, Thailand) have indicated that all methods can be used if the weather information required is available. This is because their soil-moisture distributions are alike. In addition, the model is shown to have its ability in approximately describing the phenomenon at a weekly or biweekly time scale which is desirable for agricultural engineering applications.

An Interval-Parameter Fuzzy Linear Programming with Stochastic Vertices Model for Water Resources Management under Uncertainty

Directory of Open Access Journals (Sweden)

Yan Han

2013-01-01

Full Text Available An interval-parameter fuzzy linear programming with stochastic vertices (IFLPSV method is developed for water resources management under uncertainty by coupling interval-parameter fuzzy linear programming (IFLP with stochastic programming (SP. As an extension of existing interval parameter fuzzy linear programming, the developed IFLPSV approach has advantages in dealing with dual uncertainty optimization problems, which uncertainty presents as interval parameter with stochastic vertices in both of the objective functions and constraints. The developed IFLPSV method improves upon the IFLP method by allowing dual uncertainty parameters to be incorporated into the optimization processes. A hybrid intelligent algorithm based on genetic algorithm and artificial neural network is used to solve the developed model. The developed method is then applied to water resources allocation in Beijing city of China in 2020, where water resources shortage is a challenging issue. The results indicate that reasonable solutions have been obtained, which are helpful and useful for decision makers. Although the amount of water supply from Guanting and Miyun reservoirs is declining with rainfall reduction, water supply from the South-to-North Water Transfer project will have important impact on water supply structure of Beijing city, particularly in dry year and extraordinary dry year.

Valuing a gas-fired power plant: A comparison of ordinary linear models, regime-switching approaches, and models with stochastic volatility

International Nuclear Information System (INIS)

Heydari, Somayeh; Siddiqui, Afzal

2010-01-01

Energy prices are often highly volatile with unexpected spikes. Capturing these sudden spikes may lead to more informed decision-making in energy investments, such as valuing gas-fired power plants, than ignoring them. In this paper, non-linear regime-switching models and models with mean-reverting stochastic volatility are compared with ordinary linear models. The study is performed using UK electricity and natural gas daily spot prices and suggests that with the aim of valuing a gas-fired power plant with and without operational flexibility, non-linear models with stochastic volatility, specifically for logarithms of electricity prices, provide better out-of-sample forecasts than both linear models and regime-switching models.

Thin and heavy tails in stochastic programming

Czech Academy of Sciences Publication Activity Database

Kaňková, Vlasta; Houda, Michal

2015-01-01

Roč. 51, č. 3 (2015), s. 433-456 ISSN 0023-5954 R&D Projects: GA ČR GA13-14445S Institutional support: RVO:67985556 Keywords : stochastic programming problems * stability * Wasserstein metric * L1 norm * Lipschitz property * empirical estimates * convergence rate * linear and nonlinear dependence * probability and risk constraints * stochastic dominance Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.628, year: 2015 http://library.utia.cas.cz/separaty/2015/E/kankova-0447994.pdf

Stochastic evaluation of tsunami inundation and quantitative estimating tsunami risk

International Nuclear Information System (INIS)

Fukutani, Yo; Anawat, Suppasri; Abe, Yoshi; Imamura, Fumihiko

2014-01-01

We performed a stochastic evaluation of tsunami inundation by using results of stochastic tsunami hazard assessment at the Soma port in the Tohoku coastal area. Eleven fault zones along the Japan trench were selected as earthquake faults generating tsunamis. The results show that estimated inundation area of return period about 1200 years had good agreement with that in the 2011 Tohoku earthquake. In addition, we evaluated quantitatively tsunami risk for four types of building; a reinforced concrete, a steel, a brick and a wood at the Soma port by combining the results of inundation assessment and tsunami fragility assessment. The results of quantitative estimating risk would reflect properly vulnerability of the buildings, that the wood building has high risk and the reinforced concrete building has low risk. (author)

Stochastic road excitation and control feasibility in a 2D linear tyre model

Science.gov (United States)

Rustighi, E.; Elliott, S. J.

2007-03-01

For vehicle under normal driving conditions and speeds above 30-40 km/h the dominating internal and external noise source is the sound generated by the interaction between the tyre and the road. This paper presents a simple model to predict tyre behaviour in the frequency range up to 400 Hz, where the dominant vibration is two dimensional. The tyre is modelled as an elemental system, which permits the analysis of the low-frequency tyre response when excited by distributed stochastic displacements in the contact patch. A linear model has been used to calculate the contact forces from the road roughness and thus calculate the average spectral properties of the resulting radial velocity of the tyre in one step from the spectral properties of the road roughness. Such a model has also been used to provide an estimate of the potential effect of various active control strategies for reducing the tyre vibrations.

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.

A non-linear and stochastic response surface method for Bayesian estimation of uncertainty in soil moisture simulation from a land surface model

Directory of Open Access Journals (Sweden)

F. Hossain

2004-01-01

Full Text Available This study presents a simple and efficient scheme for Bayesian estimation of uncertainty in soil moisture simulation by a Land Surface Model (LSM. The scheme is assessed within a Monte Carlo (MC simulation framework based on the Generalized Likelihood Uncertainty Estimation (GLUE methodology. A primary limitation of using the GLUE method is the prohibitive computational burden imposed by uniform random sampling of the model's parameter distributions. Sampling is improved in the proposed scheme by stochastic modeling of the parameters' response surface that recognizes the non-linear deterministic behavior between soil moisture and land surface parameters. Uncertainty in soil moisture simulation (model output is approximated through a Hermite polynomial chaos expansion of normal random variables that represent the model's parameter (model input uncertainty. The unknown coefficients of the polynomial are calculated using limited number of model simulation runs. The calibrated polynomial is then used as a fast-running proxy to the slower-running LSM to predict the degree of representativeness of a randomly sampled model parameter set. An evaluation of the scheme's efficiency in sampling is made through comparison with the fully random MC sampling (the norm for GLUE and the nearest-neighborhood sampling technique. The scheme was able to reduce computational burden of random MC sampling for GLUE in the ranges of 10%-70%. The scheme was also found to be about 10% more efficient than the nearest-neighborhood sampling method in predicting a sampled parameter set's degree of representativeness. The GLUE based on the proposed sampling scheme did not alter the essential features of the uncertainty structure in soil moisture simulation. The scheme can potentially make GLUE uncertainty estimation for any LSM more efficient as it does not impose any additional structural or distributional assumptions.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas

2017-12-27

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Stability, Empirical Estimates and Scenario Generation in Stochastic Optimization - Applications in Finance

Czech Academy of Sciences Publication Activity Database

Kaňková, Vlasta

2017-01-01

Roč. 53, č. 6 (2017), s. 1026-1046 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : stochastic programming * stochastic dominance * empirical estimates * financial applications Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/kankova-0485151.pdf

Stationary distributions of stochastic processes described by a linear neutral delay differential equation

International Nuclear Information System (INIS)

Frank, T D

2005-01-01

Stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation. The distributions are Gaussian distributions. The variances of the Gaussian distributions are either monotonically increasing or decreasing functions of the time delays. The variances become infinite when fixed points of corresponding deterministic processes become unstable. (letter to the editor)

Estimating radiative feedbacks from stochastic fluctuations in surface temperature and energy imbalance

Science.gov (United States)

Proistosescu, C.; Donohoe, A.; Armour, K.; Roe, G.; Stuecker, M. F.; Bitz, C. M.

2017-12-01

Joint observations of global surface temperature and energy imbalance provide for a unique opportunity to empirically constrain radiative feedbacks. However, the satellite record of Earth's radiative imbalance is relatively short and dominated by stochastic fluctuations. Estimates of radiative feedbacks obtained by regressing energy imbalance against surface temperature depend strongly on sampling choices and on assumptions about whether the stochastic fluctuations are primarily forced by atmospheric or oceanic variability (e.g. Murphy and Forster 2010, Dessler 2011, Spencer and Braswell 2011, Forster 2016). We develop a framework around a stochastic energy balance model that allows us to parse the different contributions of atmospheric and oceanic forcing based on their differing impacts on the covariance structure - or lagged regression - of temperature and radiative imbalance. We validate the framework in a hierarchy of general circulation models: the impact of atmospheric forcing is examined in unforced control simulations of fixed sea-surface temperature and slab ocean model versions; the impact of oceanic forcing is examined in coupled simulations with prescribed ENSO variability. With the impact of atmospheric and oceanic forcing constrained, we are able to predict the relationship between temperature and radiative imbalance in a fully coupled control simulation, finding that both forcing sources are needed to explain the structure of the lagged-regression. We further model the dependence of feedback estimates on sampling interval by considering the effects of a finite equilibration time for the atmosphere, and issues of smoothing and aliasing. Finally, we develop a method to fit the stochastic model to the short timeseries of temperature and radiative imbalance by performing a Bayesian inference based on a modified version of the spectral Whittle likelihood. We are thus able to place realistic joint uncertainty estimates on both stochastic forcing and

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

Science.gov (United States)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

On the accuracy of mode-superposition analysis of linear systems under stochastic agencies

International Nuclear Information System (INIS)

Bellomo, M.; Di Paola, M.; La Mendola, L.; Muscolino, G.

1987-01-01

This paper deals with the response of linear structures using modal reduction. The MAM (mode acceleration method) correction is extended to stochastic analysis in the stationary case. In this framework the response of the given structure must be described in a probabilistic sense and the spectral moments of the nodal response must be computed in order to obtain a full description of the vibratory stochastic phenomenon. In the deterministic analysis the response is substantially made up of two terms, one of which accounts for the dynamic response due to the lower modes while the second accounts for the contribution due to the higher modes. In stochastic analysis the nodal spectral moments are made up of three terms; the first accounts for the spectral moments of the dynamic response due to the lower modes, the second accounts for the spectral moments of input and the third accounts for the cross-spectral moments between the input and the nodal output. The analysis is applied to a 35-storey building subjected to wind multivariate environments. (orig./HP)

A termination criterion for parameter estimation in stochastic models in systems biology.

Science.gov (United States)

Zimmer, Christoph; Sahle, Sven

2015-11-01

Parameter estimation procedures are a central aspect of modeling approaches in systems biology. They are often computationally expensive, especially when the models take stochasticity into account. Typically parameter estimation involves the iterative optimization of an objective function that describes how well the model fits some measured data with a certain set of parameter values. In order to limit the computational expenses it is therefore important to apply an adequate stopping criterion for the optimization process, so that the optimization continues at least until a reasonable fit is obtained, but not much longer. In the case of stochastic modeling, at least some parameter estimation schemes involve an objective function that is itself a random variable. This means that plain convergence tests are not a priori suitable as stopping criteria. This article suggests a termination criterion suited to optimization problems in parameter estimation arising from stochastic models in systems biology. The termination criterion is developed for optimization algorithms that involve populations of parameter sets, such as particle swarm or evolutionary algorithms. It is based on comparing the variance of the objective function over the whole population of parameter sets with the variance of repeated evaluations of the objective function at the best parameter set. The performance is demonstrated for several different algorithms. To test the termination criterion we choose polynomial test functions as well as systems biology models such as an Immigration-Death model and a bistable genetic toggle switch. The genetic toggle switch is an especially challenging test case as it shows a stochastic switching between two steady states which is qualitatively different from the model behavior in a deterministic model. Copyright © 2015. Published by Elsevier Ireland Ltd.

Error estimates for discretized quantum stochastic differential inclusions

International Nuclear Information System (INIS)

Ayoola, E.O.

2001-09-01

This paper is concerned with the error estimates involved in the solution of a discrete approximation of a quantum stochastic differential inclusion (QSDI). Our main results rely on certain properties of the averaged modulus of continuity for multivalued sesquilinear forms associated with QSDI. We obtained results concerning the estimates of the Hausdorff distance between the set of solutions of the QSDI and the set of solutions of its discrete approximation. This extend the results of Dontchev and Farkhi concerning classical differential inclusions to the present noncommutative Quantum setting involving inclusions in certain locally convex space. (author)

Gompertzian stochastic model with delay effect to cervical cancer growth

International Nuclear Information System (INIS)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-01-01

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits

Gompertzian stochastic model with delay effect to cervical cancer growth

Energy Technology Data Exchange (ETDEWEB)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

A heterogeneous stochastic FEM framework for elliptic PDEs

International Nuclear Information System (INIS)

Hou, Thomas Y.; Liu, Pengfei

2015-01-01

We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage

A separation theorem for the stochastic sampled-data LQG problem. [control of continuous linear plant disturbed by white noise

Science.gov (United States)

Halyo, N.; Caglayan, A. K.

1976-01-01

This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.

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

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

Non-linear and signal energy optimal asymptotic filter design

Directory of Open Access Journals (Sweden)

Josef Hrusak

2003-10-01

Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.

Probability, Statistics, and Stochastic Processes

CERN Document Server

Olofsson, Peter

2012-01-01

This book provides a unique and 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.  The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and

Linear stochastic systems a geometric approach to modeling, estimation and identification

CERN Document Server

Lindquist, Anders

2015-01-01

This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of pas...

Estimation of parameters in Shot-Noise-Driven Doubly Stochastic Poisson processes using the EM algorithm--modeling of pre- and postsynaptic spike trains.

Science.gov (United States)

Mino, H

2007-01-01

To estimate the parameters, the impulse response (IR) functions of some linear time-invariant systems generating intensity processes, in Shot-Noise-Driven Doubly Stochastic Poisson Process (SND-DSPP) in which multivariate presynaptic spike trains and postsynaptic spike trains can be assumed to be modeled by the SND-DSPPs. An explicit formula for estimating the IR functions from observations of multivariate input processes of the linear systems and the corresponding counting process (output process) is derived utilizing the expectation maximization (EM) algorithm. The validity of the estimation formula was verified through Monte Carlo simulations in which two presynaptic spike trains and one postsynaptic spike train were assumed to be observable. The IR functions estimated on the basis of the proposed identification method were close to the true IR functions. The proposed method will play an important role in identifying the input-output relationship of pre- and postsynaptic neural spike trains in practical situations.

Stochastic Response of an Inclined Shallow Cable with Linear Viscous Dampers under Stochastic Excitation

DEFF Research Database (Denmark)

Zhou, Qiang; Nielsen, Søren R.K.; Qu, Weilian

2010-01-01

Considering the coupling between the in-plane and out-of-plane vibration, the stochastic response of an inclined shallow cable with linear viscous dampers subjected to Gaussian white noise excitation is investigated in this paper. Selecting the static deflection shape due to a concentrated force...... together with the C-type Gram-Charlier expansion with a fourth-order closure are applied to obtain statistical moments, power spectral density and probabilistic density function of the cable response, whose availability is verified by Monte Carlo method. Taking a typical cable as an example, the influence...... of several factors, which include excitation level and direction as well as damper size, on the dynamic response of the cable is extensively investigated. It is found that the sum of mean square in-plane and out-of-plane displacement is primarily independent of the load direction when the excitation level...

Algorithms for non-linear M-estimation

DEFF Research Database (Denmark)

Madsen, Kaj; Edlund, O; Ekblom, H

1997-01-01

In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

International Nuclear Information System (INIS)

Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim

2013-01-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier Inc.

A remark on empirical estimates in multistage stochastic programming

Czech Academy of Sciences Publication Activity Database

Kaňková, Vlasta

2002-01-01

Roč. 9, č. 17 (2002), s. 31-50 ISSN 1212-074X R&D Projects: GA ČR GA402/01/0539; GA ČR GA402/02/1015; GA ČR GA402/01/0034 Institutional research plan: CEZ:AV0Z1075907 Keywords : multistage stochastic programming * empirical estimates * Markov dependence Subject RIV: BB - Applied Statistics, Operational Research

An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management

DEFF Research Database (Denmark)

Escudero, Laureano F.; Monge, Juan Francisco; Morales, Dolores Romero

2015-01-01

In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multist...

Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

Directory of Open Access Journals (Sweden)

Li Chen

2012-01-01

stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

Science.gov (United States)

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

Nonlinear filtering and smoothing an introduction to martingales, stochastic integrals and estimation

CERN Document Server

Krishnan, Venkatarama

2005-01-01

Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value.After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping time

SLFP: a stochastic linear fractional programming approach for sustainable waste management.

Science.gov (United States)

Zhu, H; Huang, G H

2011-12-01

A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

Stochastic growth logistic model with aftereffect for batch fermentation process

Energy Technology Data Exchange (ETDEWEB)

Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

Science.gov (United States)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

International Nuclear Information System (INIS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-01-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits

Modeling stochastic frontier based on vine copulas

Science.gov (United States)

Constantino, Michel; Candido, Osvaldo; Tabak, Benjamin M.; da Costa, Reginaldo Brito

2017-11-01

This article models a production function and analyzes the technical efficiency of listed companies in the United States, Germany and England between 2005 and 2012 based on the vine copula approach. Traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry. The proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution. Using data on product, capital and labor, we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes. This production vine copula predicts the value added by firms with given capital and labor in a probabilistic way. It thereby stands in sharp contrast to the production function, where the output of firms is completely deterministic. The results show that, on average, S&P500 companies are more efficient than companies listed in England and Germany, which presented similar average efficiency coefficients. For comparative purposes, the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods, traditional and frontier-vine, opening new paths of non-linear research.

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)

Linear kinetic theory and particle transport in stochastic mixtures

International Nuclear Information System (INIS)

Pomraning, G.C.

1994-03-01

The primary goal in this research is to develop a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. The statistics considered correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components of the mixture. The mixing statistics studied are Markovian as well as more general statistics, such as renewal processes. A further goal of this work is to demonstrate the applicability of the formalism to real world engineering problems. This three year program was initiated June 15, 1993 and has been underway nine months. Many significant results have been obtained, both in the formalism development and in representative applications. These results are summarized by listing the archival publications resulting from this grant, including the abstracts taken directly from the papers

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

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

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

Directory of Open Access Journals (Sweden)

Biçer Cenker

2016-01-01

Full Text Available In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.

Enhanced Performance Controller Design for Stochastic Systems by Adding Extra State Estimation onto the Existing Closed Loop Control

Energy Technology Data Exchange (ETDEWEB)

Zhou, Yuyang; Zhang, Qichun; Wang, Hong

2016-08-30

To enhance the performance of the tracking property , this paper presents a novel control algorithm for a class of linear dynamic stochastic systems with unmeasurable states, where the performance enhancement loop is established based on Kalman filter. Without changing the existing closed loop with the PI controller, the compensative controller is designed to minimize the variances of the tracking errors using the estimated states and the propagation of state variances. Moreover, the stability of the closed-loop systems has been analyzed in the mean-square sense. A simulated example is included to show the effectiveness of the presented control algorithm, where encouraging results have been obtained.

Non-parametric system identification from non-linear stochastic response

DEFF Research Database (Denmark)

Rüdinger, Finn; Krenk, Steen

2001-01-01

An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable...... of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method...

Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014

Science.gov (United States)

Klos, Anna; Bogusz, Janusz; Moreaux, Guilhem

2017-11-01

This paper focuses on the investigation of the deterministic and stochastic parts of the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) weekly time series aligned to the newest release of ITRF2014. A set of 90 stations was divided into three groups depending on when the data were collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations and a stochastic part, all being estimated with maximum likelihood estimation. We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations. The quality of the most recent data has significantly improved. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. Among several tested models, the power-law process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from an autoregressive process to pure power-law noise with few stations characterised by a positive spectral index. For the latest observations, the medians of the velocity errors were equal to 0.3, 0.3 and 0.4 mm/year, respectively, for the North, East and Up components. In the best cases, a velocity uncertainty of DORIS sites of 0.1 mm/year is achievable when the appropriate coloured noise model is taken into consideration.

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

Science.gov (United States)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Linear theory for filtering nonlinear multiscale systems with model error.

Science.gov (United States)

Berry, Tyrus; Harlim, John

2014-07-08

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

Energy Technology Data Exchange (ETDEWEB)

Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies

2018-03-29

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

Estimation and Control for Linear Systems with Additive Cauchy Noise

Science.gov (United States)

2013-12-17

man & Hall, New York, 1994. [11] J. L. Speyer and W. H. Chung, Stochastic Processes, Estimation, and Control, SIAM, 2008. [12] Nassim N. Taleb ...Gaussian control algorithms. 18 4 References [1] N. N. Taleb . The Black Swan: The Impact of the Highly Improbable...the multivariable system. The estimator was then evaluated numerically for a third-order example. REFERENCES [1] N. N. Taleb , The Black Swan: The

Stochastic quantization and gauge-fixing of the linearized gravitational field

International Nuclear Information System (INIS)

Hueffel, H.; Rumpf, H.

1984-01-01

Due to the indefiniteness of the Euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gravitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization. (Author)

A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions

KAUST Repository

Butler, T.; Dawson, C.; Wildey, T.

2011-01-01

We develop computable a posteriori error estimates for linear functionals of a solution to a general nonlinear stochastic differential equation with random model/source parameters. These error estimates are based on a variational analysis applied to stochastic Galerkin methods for forward and adjoint problems. The result is a representation for the error estimate as a polynomial in the random model/source parameter. The advantage of this method is that we use polynomial chaos representations for the forward and adjoint systems to cheaply produce error estimates by simple evaluation of a polynomial. By comparison, the typical method of producing such estimates requires repeated forward/adjoint solves for each new choice of random parameter. We present numerical examples showing that there is excellent agreement between these methods. © 2011 Society for Industrial and Applied Mathematics.

Improved linear least squares estimation using bounded data uncertainty

KAUST Repository

Ballal, Tarig

2015-04-01

This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.

Improved linear least squares estimation using bounded data uncertainty

KAUST Repository

Ballal, Tarig; Al-Naffouri, Tareq Y.

2015-01-01

This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.

Stationary stochastic processes theory and applications

CERN Document Server

Lindgren, Georg

2012-01-01

Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...

Optimal difference-based estimation for partially linear models

KAUST Repository

Zhou, Yuejin; Cheng, Yebin; Dai, Wenlin; Tong, Tiejun

2017-01-01

Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.

Optimal difference-based estimation for partially linear models

KAUST Repository

Zhou, Yuejin

2017-12-16

Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.

Stochastic Corn Yield Response Functions to Nitrogen for Corn after Corn, Corn after Cotton, and Corn after Soybeans

OpenAIRE

Boyer, Christopher N.; Larson, James A.; Roberts, Roland K.; McClure, Angela T.; Tyler, Donald D.; Zhou, Vivian

2013-01-01

Deterministic and stochastic yield response plateau functions were estimated to determine the expected profit-maximizing nitrogen rates, yields, and net returns for corn grown after corn, cotton, and soybeans. The stochastic response functions were more appropriate than their deterministic counterparts, and the linear response stochastic plateau described the data the best. The profit-maximizing nitrogen rates were similar for corn after corn, cotton, and soybeans, but relative to corn after ...

Robust estimation for partially linear models with large-dimensional covariates.

Science.gov (United States)

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

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

Global CO2 efficiency: Country-wise estimates using a stochastic cost frontier

International Nuclear Information System (INIS)

Herrala, Risto; Goel, Rajeev K.

2012-01-01

This paper examines global carbon dioxide (CO 2 ) efficiency by employing a stochastic cost frontier analysis of about 170 countries in 1997 and 2007. The main contribution lies in providing a new approach to environmental efficiency estimation, in which the efficiency estimates quantify the distance from the policy objective of minimum emissions. We are able to examine a very large pool of nations and provide country-wise efficiency estimates. We estimate three econometric models, corresponding with alternative interpretations of the Cancun vision (Conference of the Parties 2011). The models reveal progress in global environmental efficiency during a preceding decade. The estimates indicate vast differences in efficiency levels, and efficiency changes across countries. The highest efficiency levels are observed in Africa and Europe, while the lowest are clustered around China. The largest efficiency gains were observed in central and eastern Europe. CO 2 efficiency also improved in the US and China, the two largest emitters, but their ranking in terms of CO 2 efficiency deteriorated. Policy implications are discussed. - Highlights: ► We estimate global environmental efficiency in line with the Cancun vision, using a stochastic cost frontier. ► The study covers 170 countries during a 10 year period, ending in 2007. ► The biggest improvements occurred in Europe, and efficiency falls in South America. ► The efficiency ranking of US and China, the largest emitters, deteriorated. ► In 2007, highest efficiency was observed in Africa and Europe, and the lowest around China.

Linearized motion estimation for articulated planes.

Science.gov (United States)

Datta, Ankur; Sheikh, Yaser; Kanade, Takeo

2011-04-01

In this paper, we describe the explicit application of articulation constraints for estimating the motion of a system of articulated planes. We relate articulations to the relative homography between planes and show that these articulations translate into linearized equality constraints on a linear least-squares system, which can be solved efficiently using a Karush-Kuhn-Tucker system. The articulation constraints can be applied for both gradient-based and feature-based motion estimation algorithms and to illustrate this, we describe a gradient-based motion estimation algorithm for an affine camera and a feature-based motion estimation algorithm for a projective camera that explicitly enforces articulation constraints. We show that explicit application of articulation constraints leads to numerically stable estimates of motion. The simultaneous computation of motion estimates for all of the articulated planes in a scene allows us to handle scene areas where there is limited texture information and areas that leave the field of view. Our results demonstrate the wide applicability of the algorithm in a variety of challenging real-world cases such as human body tracking, motion estimation of rigid, piecewise planar scenes, and motion estimation of triangulated meshes.

Estimating linear effects in ANOVA designs: the easy way.

Science.gov (United States)

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

2012-09-01

Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.

Linear dynamical quantum systems analysis, synthesis, and control

CERN Document Server

Nurdin, Hendra I

2017-01-01

This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics ...

Improved estimation of hydraulic conductivity by combining stochastically simulated hydrofacies with geophysical data.

Science.gov (United States)

Zhu, Lin; Gong, Huili; Chen, Yun; Li, Xiaojuan; Chang, Xiang; Cui, Yijiao

2016-03-01

Hydraulic conductivity is a major parameter affecting the output accuracy of groundwater flow and transport models. The most commonly used semi-empirical formula for estimating conductivity is Kozeny-Carman equation. However, this method alone does not work well with heterogeneous strata. Two important parameters, grain size and porosity, often show spatial variations at different scales. This study proposes a method for estimating conductivity distributions by combining a stochastic hydrofacies model with geophysical methods. The Markov chain model with transition probability matrix was adopted to re-construct structures of hydrofacies for deriving spatial deposit information. The geophysical and hydro-chemical data were used to estimate the porosity distribution through the Archie's law. Results show that the stochastic simulated hydrofacies model reflects the sedimentary features with an average model accuracy of 78% in comparison with borehole log data in the Chaobai alluvial fan. The estimated conductivity is reasonable and of the same order of magnitude of the outcomes of the pumping tests. The conductivity distribution is consistent with the sedimentary distributions. This study provides more reliable spatial distributions of the hydraulic parameters for further numerical modeling.

Stochastic cost estimating in repository life-cycle cost analysis

International Nuclear Information System (INIS)

Tzemos, S.; Dippold, D.

1986-01-01

The conceptual development, the design, and the final construction and operation of a nuclear repository span many decades. Given this lengthy time frame, it is quite challenging to obtain a good approximation of the repository life-cycle cost. One can deal with this challenge by using an analytic method, the method of moments, to explicitly assess the uncertainty of the estimate. A series expansion is used to approximate the uncertainty distribution of the cost estimate. In this paper, the moment methodology is derived and is illustrated through a numerical example. The range of validity of the approximation is discussed. The method of moments is compared to the traditional stochastic cost estimating methods and found to provide more and better information on cost uncertainty. The tow methods converge to identical results as the number of convolved variables increases and approaches the range where the central limit theorem is valid

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.

Empirical Estimates in Stochastic Optimization via Distribution Tails

Czech Academy of Sciences Publication Activity Database

Kaňková, Vlasta

2010-01-01

Roč. 46, č. 3 (2010), s. 459-471 ISSN 0023-5954. [International Conference on Mathematical Methods in Economy and Industry. České Budějovice, 15.06.2009-18.06.2009] R&D Projects: GA ČR GA402/07/1113; GA ČR(CZ) GA402/08/0107; GA MŠk(CZ) LC06075 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic programming problems * Stability * Wasserstein metric * L_1 norm * Lipschitz property * Empirical estimates * Convergence rate * Exponential tails * Heavy tails * Pareto distribution * Risk functional * Empirical quantiles Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.461, year: 2010

Stochastic Models in the DORIS Position Time Series: Estimates from the IDS Contribution to the ITRF2014

Science.gov (United States)

Klos, A.; Bogusz, J.; Moreaux, G.

2017-12-01

This research focuses on the investigation of the deterministic and stochastic parts of the DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) weekly coordinate time series from the IDS contribution to the ITRF2014A set of 90 stations was divided into three groups depending on when the data was collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations (these three sum up to produce the Polynomial Trend Model) and a stochastic part, all being resolved with Maximum Likelihood Estimation (MLE). We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations, meaning that the most recent data are the most reliable ones. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. We examined five different noise models to be applied to the stochastic part of the DORIS time series: a pure white noise (WN), a pure power-law noise (PL), a combination of white and power-law noise (WNPL), an autoregressive process of first order (AR(1)) and a Generalized Gauss Markov model (GGM). From our study it arises that the PL process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from AR(1) to pure PL with few stations characterized by a positive spectral index.

Stochastic lag time in nucleated linear self-assembly

Energy Technology Data Exchange (ETDEWEB)

Tiwari, Nitin S. [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Schoot, Paul van der [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)

2016-06-21

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerization reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerization commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway.

On parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations

International Nuclear Information System (INIS)

Phan Thanh An; Phan Le Na; Ngo Quoc Chung

2004-05-01

We describe a practical implementation for finding parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations based on Korenevskij and Mitropolskij's sufficient condition and our sufficient conditions. Numerical results show that all of these sufficient conditions are crucial in the implementation. (author)

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.

Online prediction and control in nonlinear stochastic systems

DEFF Research Database (Denmark)

Nielsen, Torben Skov

2002-01-01

speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...

A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

Directory of Open Access Journals (Sweden)

Wang Xiaoxiao

2018-04-01

Full Text Available A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014 74-87 and Li et al. (Linear and Multilinear Algebra 63(11 (2015 2159-2170 for estimating the moduli of subdominant eigenvalues.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

Science.gov (United States)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Estimating linear temporal trends from aggregated environmental monitoring data

Science.gov (United States)

Erickson, Richard A.; Gray, Brian R.; Eager, Eric A.

2017-01-01

Trend estimates are often used as part of environmental monitoring programs. These trends inform managers (e.g., are desired species increasing or undesired species decreasing?). Data collected from environmental monitoring programs is often aggregated (i.e., averaged), which confounds sampling and process variation. State-space models allow sampling variation and process variations to be separated. We used simulated time-series to compare linear trend estimations from three state-space models, a simple linear regression model, and an auto-regressive model. We also compared the performance of these five models to estimate trends from a long term monitoring program. We specifically estimated trends for two species of fish and four species of aquatic vegetation from the Upper Mississippi River system. We found that the simple linear regression had the best performance of all the given models because it was best able to recover parameters and had consistent numerical convergence. Conversely, the simple linear regression did the worst job estimating populations in a given year. The state-space models did not estimate trends well, but estimated population sizes best when the models converged. We found that a simple linear regression performed better than more complex autoregression and state-space models when used to analyze aggregated environmental monitoring data.

Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation

International Nuclear Information System (INIS)

Gershgorin, B.; Harlim, J.; Majda, A.J.

2010-01-01

The filtering and predictive skill for turbulent signals is often limited by the lack of information about the true dynamics of the system and by our inability to resolve the assumed dynamics with sufficiently high resolution using the current computing power. The standard approach is to use a simple yet rich family of constant parameters to account for model errors through parameterization. This approach can have significant skill by fitting the parameters to some statistical feature of the true signal; however in the context of real-time prediction, such a strategy performs poorly when intermittent transitions to instability occur. Alternatively, we need a set of dynamic parameters. One strategy for estimating parameters on the fly is a stochastic parameter estimation through partial observations of the true signal. In this paper, we extend our newly developed stochastic parameter estimation strategy, the Stochastic Parameterization Extended Kalman Filter (SPEKF), to filtering sparsely observed spatially extended turbulent systems which exhibit abrupt stability transition from time to time despite a stable average behavior. For our primary numerical example, we consider a turbulent system of externally forced barotropic Rossby waves with instability introduced through intermittent negative damping. We find high filtering skill of SPEKF applied to this toy model even in the case of very sparse observations (with only 15 out of the 105 grid points observed) and with unspecified external forcing and damping. Additive and multiplicative bias corrections are used to learn the unknown features of the true dynamics from observations. We also present a comprehensive study of predictive skill in the one-mode context including the robustness toward variation of stochastic parameters, imperfect initial conditions and finite ensemble effect. Furthermore, the proposed stochastic parameter estimation scheme applied to the same spatially extended Rossby wave system demonstrates

The Expected Loss in the Discretization of Multistage Stochastic Programming Problems - Estimation and Convergence Rate

Czech Academy of Sciences Publication Activity Database

Šmíd, Martin

2009-01-01

Roč. 165, č. 1 (2009), s. 29-45 ISSN 0254-5330 R&D Projects: GA ČR GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : multistage stochastic programming problems * approximation * discretization * Monte Carlo Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.961, year: 2009 http://library.utia.cas.cz/separaty/2008/E/smid-the expected loss in the discretization of multistage stochastic programming problems - estimation and convergence rate.pdf

Quantization of O(N) non-linear sigma models as the stochastic motion on Ssup(N-1)

International Nuclear Information System (INIS)

Aldazabal, G.; Parga, N.

1983-09-01

We obtain the Langevin equations for the stochastic quantization of the O(N) non-linear sigma model by studying the random (Gaussian) motion on the sphere Ssup(N-1). We prove the equivalence of this procedure with a different one where the random forces are elements of the O(N) algebra. A proof that our approach yields in the equilibrium regime the quantum field theory is also given. (author)

Stochastic optimal charging of electric-drive vehicles with renewable energy

International Nuclear Information System (INIS)

Pantoš, Miloš

2011-01-01

The paper presents the stochastic optimization algorithm that may eventually be used by electric energy suppliers to coordinate charging of electric-drive vehicles (EDVs) in order to maximize the use of renewable energy in transportation. Due to the stochastic nature of transportation patterns, the Monte Carlo simulation is applied to model uncertainties presented by numerous scenarios. To reduce the problem complexity, the simulated driving patterns are not individually considered in the optimization but clustered into fleets using the GAMS/SCENRED tool. Uncertainties of production of renewable energy sources (RESs) are presented by statistical central moments that are further considered in Hong’s 2-point + 1 estimation method in order to define estimate points considered in the optimization. Case studies illustrate the application of the proposed optimization in achieving maximal exploitation of RESs in transportation by EDVs. -- Highlights: ► Optimization model for EDV charging applying linear programming. ► Formation of EDV fleets based on the driving patterns assessment applying the GAMS/SCENRED. ► Consideration of uncertainties of RES production and energy prices in the market. ► Stochastic optimization. ► Application of Hong’s 2-point + 1 estimation method.

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

2015-01-01

From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions.

Science.gov (United States)

Aralis, Hilary; Brookmeyer, Ron

2017-01-01

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

International Nuclear Information System (INIS)

Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa

2015-01-01

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

Energy Technology Data Exchange (ETDEWEB)

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr [Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7) UFR de Mathématiques - Bât. Sophie Germain (France); Picarelli, Athena, E-mail: athena.picarelli@inria.fr [Projet Commands, INRIA Saclay & ENSTA ParisTech (France); Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr [Unité de Mathématiques appliquées (UMA), ENSTA ParisTech (France)

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.

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)

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.

Stochastic thermodynamics

Science.gov (United States)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response

Fixation of Cs to marine sediments estimated by a stochastic modelling approach.

Science.gov (United States)

Børretzen, Peer; Salbu, Brit

2002-01-01

Dumping of nuclear waste in the Kara Sea represents a potential source of radioactive contamination to the Arctic Seas in the future. The mobility of 137Cs ions leached from the waste will depend on the interactions with sediment particles. Whether sediments will act as a continuous permanent sink for released 137Cs, or contaminated sediments will serve as a diffuse source of 137Cs in the future, depends on the interaction kinetics and binding mechanisms involved. The main purpose of this paper is to study the performance of different stochastic models using kinetic information to estimate the time needed for Cs ions to become irreversibly fixed within the sediments. The kinetic information was obtained from 134Cs tracer sorption and desorption (sequential extractions) experiments, conducted over time, using sediments from the Stepovogo Fjord waste dumping site, on the east coast of Novaya Zemlya. Results show that 134Cs ions interact rapidly with the surfaces of the Stepovogo sediment, with an estimated distribution coefficient Kd(eq) of 300 ml/g (or 13m2/g), and the 134Cs ions are increasingly irreversibly fixed to the sediment over time. For the first time, stochastic theory has been utilised for sediment-seawater systems to estimate the mean residence times (MRTs) of Cs ions in operationally defined sediment phases described by compartment models. In the present work, two different stochastic models (i) a Markov process model (MP) being analogous to deterministic compartment models, and (ii) a semi-Markov process model (SMP) which should be physically more relevant for inhomogeneous systems, have been compared. As similar results were obtained using the two models, the less complicated MP model was utilised to predict the time needed for an average Cs ion to become irreversibly fixed in the Stepovogo sediments. According the model, approximately 1100 days of contact time between Cs ions and sediments is needed before 50% of the 134Cs ion becomes fixed in the

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.

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)

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

Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

Directory of Open Access Journals (Sweden)

Bingyong Yan

2014-01-01

Full Text Available A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs. Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.

Stochastic-based resource expansion planning for a grid-connected microgrid using interval linear programming

International Nuclear Information System (INIS)

Shaban Boloukat, Mohammad Hadi; Akbari Foroud, Asghar

2016-01-01

This paper represents a stochastic approach for long-term optimal resource expansion planning of a grid-connected microgrid (MG) containing different technologies as intermittent renewable energy resources, energy storage systems and thermal resources. Maximizing profit and reliability, along with minimizing investment and operation costs, are major objectives which have been considered in this model. Also, the impacts of intermittency and uncertainty in renewable energy resources were investigated. The interval linear programming (ILP) was applied for modelling inherent stochastic nature of the renewable energy resources. ILP presents some superiority in modelling of uncertainties in MG planning. The problem was formulated as a mixed-integer linear programming. It has been demonstrated previously that the benders decomposition (BD) served as an effective tool for solving such problems. BD divides the original problem into a master (investment) problem and operation and reliability subproblems. In this paper a multiperiod MG planning is presented, considering life time, maximum penetration limit of each technology, interest rate, capital recovery factor and investment fund. Real-time energy exchange with the utility is covered, with a consideration of variable tariffs at different load blocks. The presented approach can help MG planners to adopt best decision under various uncertainty levels based on their budgetary policies. - Highlights: • Considering uncertain nature of the renewable resources with applying ILP. • Considering the effect of intermittency of renewable in MG planning. • Multiobjective MG planning problem which covers cost, profit and reliability. • Multiperiod approach for MG planning considering life time and MPL of technologies. • Presenting real-time energy exchange with the utility considering variable tariffs.

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

Energy Technology Data Exchange (ETDEWEB)

Chen, Kho Chia; Kane, Ibrahim Lawal; Rahman, Haliza Abd [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru (Malaysia); Bahar, Arifah [UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310, Johor Bahru and Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru (Malaysia); Ting, Chee-Ming [Center for Biomedical Engineering, Universiti Teknologi Malaysia, 81310, Johor Bahru (Malaysia)

2015-02-03

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well.

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

Science.gov (United States)

Chen, Kho Chia; Bahar, Arifah; Kane, Ibrahim Lawal; Ting, Chee-Ming; Rahman, Haliza Abd

2015-02-01

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well.

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

International Nuclear Information System (INIS)

Chen, Kho Chia; Kane, Ibrahim Lawal; Rahman, Haliza Abd; Bahar, Arifah; Ting, Chee-Ming

2015-01-01

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well

Trapped modes in linear quantum stochastic networks with delays

Energy Technology Data Exchange (ETDEWEB)

Tabak, Gil [Stanford University, Department of Applied Physics, Stanford, CA (United States); Mabuchi, Hideo

2016-12-15

Networks of open quantum systems with feedback have become an active area of research for applications such as quantum control, quantum communication and coherent information processing. A canonical formalism for the interconnection of open quantum systems using quantum stochastic differential equations (QSDEs) has been developed by Gough, James and co-workers and has been used to develop practical modeling approaches for complex quantum optical, microwave and optomechanical circuits/networks. In this paper we fill a significant gap in existing methodology by showing how trapped modes resulting from feedback via coupled channels with finite propagation delays can be identified systematically in a given passive linear network. Our method is based on the Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued functions, which has been applied in the past to analog electronic networks. Our results provide a basis for extending the Quantum Hardware Description Language (QHDL) framework for automated quantum network model construction (Tezak et al. in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 370(1979):5270-5290, 2012) to efficiently treat scenarios in which each interconnection of components has an associated signal propagation time delay. (orig.)

Estimating monotonic rates from biological data using local linear regression.

Science.gov (United States)

Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

2017-03-01

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

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,...

Event-Based $H_\\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises.

Science.gov (United States)

Sheng, Li; Wang, Zidong; Zou, Lei; Alsaadi, Fuad E

2017-10-01

In this paper, the event-based finite-horizon H ∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H ∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

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.)

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

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-10-01

The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result 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 approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu [Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States); Elman, Howard C., E-mail: elman@cs.umd.edu [Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 (United States)

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.

Estimation of some stochastic models used in reliability engineering

International Nuclear Information System (INIS)

Huovinen, T.

1989-04-01

The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a beta-binomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gamma-poisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilizing point processes. Here we consider the statistical analysis of non-homogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method

Chance Constrained Input Relaxation to Congestion in Stochastic DEA. An Application to Iranian Hospitals.

Science.gov (United States)

Kheirollahi, Hooshang; Matin, Behzad Karami; Mahboubi, Mohammad; Alavijeh, Mehdi Mirzaei

2015-01-01

This article developed an approached model of congestion, based on relaxed combination of inputs, in stochastic data envelopment analysis (SDEA) with chance constrained programming approaches. Classic data envelopment analysis models with deterministic data have been used by many authors to identify congestion and estimate its levels; however, data envelopment analysis with stochastic data were rarely used to identify congestion. This article used chance constrained programming approaches to replace stochastic models with "deterministic equivalents". This substitution leads us to non-linear problems that should be solved. Finally, the proposed method based on relaxed combination of inputs was used to identify congestion input in six Iranian hospital with one input and two outputs in the period of 2009 to 2012.

Dimension Reduction and Discretization in Stochastic Problems by Regression Method

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

1996-01-01

The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ...

Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

Directory of Open Access Journals (Sweden)

Shelton Peiris

2017-12-01

Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.

Stochastic Optimization Model to STudy the Operational Impacts of High Wind Penetrations in Ireland

DEFF Research Database (Denmark)

Meibom, Peter; Barth, R.; Hasche, B.

2011-01-01

A stochastic mixed integer linear optimization scheduling model minimizing system operation costs and treating load and wind power production as stochastic inputs is presented. The schedules are updated in a rolling manner as more up-to-date information becomes available. This is a fundamental...... change relative to day-ahead unit commitment approaches. The need for reserves dependent on forecast horizon and share of wind power has been estimated with a statistical model combining load and wind power forecast errors with scenarios of forced outages. The model is used to study operational impacts...

Reliability estimation of structures under stochastic loading—A case study on nuclear piping

International Nuclear Information System (INIS)

Hari Prasad, M.; Rami Reddy, G.; Dubey, P.N.; Srividya, A.; Verma, A.K.

2013-01-01

Highlights: ► Structures are generally subjected to different types of loadings. ► One such type of loading is random sequence and has been treated as a stochastic fatigue loading. ► In this methodology both stress amplitude and number of cycles to failure have been considered as random variables. ► The methodology has been demonstrated with a case study on nuclear piping. ► The failure probability of piping has been estimated as a function of time. - Abstract: Generally structures are subjected to different types of loadings throughout their life time. These loads can be either discrete in nature or continuous in nature and also these can be either stationary or non stationary processes. This means that the structural reliability analysis not only considers random variables but also considers random variables which are functions of time, referred to as stochastic processes. A stochastic process can be viewed as a family of random variables. When a structure is subjected to a random loading, based on the stresses developed in the structure and failure criteria the failure probability can be estimated. In practice the structures are designed with higher factor of safety to take care of such random loads. In such cases the structure will fail only when the random loads are cyclic in nature. In traditional reliability analysis, the variation in the load is treated as a random variable and to account for the number of occurrences of the loading the concept of extreme value theory is used. But with this method one is neglecting the damage accumulation that will take place from one loading to another loading. Hence, in this paper, a new way of dealing with these types of problems has been discussed by using the concept of stochastic fatigue loading. The random loading has been considered as earthquake loading. The methodology has been demonstrated with a case study on nuclear power plant piping.

Uncertainty quantification in a chemical system using error estimate-based mesh adaption

International Nuclear Information System (INIS)

Mathelin, Lionel; Le Maitre, Olivier P.

2012-01-01

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows. (authors)

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

Stochastic Stability of Endogenous Growth: Theory and Applications

OpenAIRE

Boucekkine, Raouf; Pintus, Patrick; Zou, Benteng

2015-01-01

We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differen- tial equations to which several stochastic endogenous growth models reduce. Second, we apply the mathematical theory to two models, starting with the stochastic AK model. It’s shown that in this case exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncerta...

Economic policy optimization based on both one stochastic model and the parametric control theory

Science.gov (United States)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

SNR Estimation in Linear Systems with Gaussian Matrices

KAUST Repository

Suliman, Mohamed Abdalla Elhag; Alrashdi, Ayed; Ballal, Tarig; Al-Naffouri, Tareq Y.

2017-01-01

This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.

SNR Estimation in Linear Systems with Gaussian Matrices

KAUST Repository

Suliman, Mohamed Abdalla Elhag

2017-09-27

This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.

Performances Of Estimators Of Linear Models With Autocorrelated ...

African Journals Online (AJOL)

The performances of five estimators of linear models with Autocorrelated error terms are compared when the independent variable is autoregressive. The results reveal that the properties of the estimators when the sample size is finite is quite similar to the properties of the estimators when the sample size is infinite although ...

Stochastic B-series and order conditions for exponential integrators

DEFF Research Database (Denmark)

Arara, Alemayehu Adugna; Debrabant, Kristian; Kværnø, Anne

2018-01-01

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential integrators. The resulting...

Unstable volatility functions: the break preserving local linear estimator

DEFF Research Database (Denmark)

Casas, Isabel; Gijbels, Irene

The objective of this paper is to introduce the break preserving local linear (BPLL) estimator for the estimation of unstable volatility functions. Breaks in the structure of the conditional mean and/or the volatility functions are common in Finance. Markov switching models (Hamilton, 1989......) and threshold models (Lin and Terasvirta, 1994) are amongst the most popular models to describe the behaviour of data with structural breaks. The local linear (LL) estimator is not consistent at points where the volatility function has a break and it may even report negative values for finite samples...

Linear Covariance Analysis and Epoch State Estimators

Science.gov (United States)

Markley, F. Landis; Carpenter, J. Russell

2014-01-01

This paper extends in two directions the results of prior work on generalized linear covariance analysis of both batch least-squares and sequential estimators. The first is an improved treatment of process noise in the batch, or epoch state, estimator with an epoch time that may be later than some or all of the measurements in the batch. The second is to account for process noise in specifying the gains in the epoch state estimator. We establish the conditions under which the latter estimator is equivalent to the Kalman filter.

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

International Nuclear Information System (INIS)

Brown, Kristen A.; Harlim, John

2013-01-01

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable

Pricing stock options under stochastic volatility and interest rates with efficient method of moments estimation

NARCIS (Netherlands)

Jiang, George J.; Sluis, Pieter J. van der

1999-01-01

While the stochastic volatility (SV) generalization has been shown to improve the explanatory power over the Black-Scholes model, empirical implications of SV models on option pricing have not yet been adequately tested. The purpose of this paper is to first estimate a multivariate SV model using

Filtering and control of stochastic jump hybrid systems

CERN Document Server

Yao, Xiuming; Zheng, Wei Xing

2016-01-01

This book presents recent research work on stochastic jump hybrid systems. Specifically, the considered stochastic jump hybrid systems include Markovian jump Ito stochastic systems, Markovian jump linear-parameter-varying (LPV) systems, Markovian jump singular systems, Markovian jump two-dimensional (2-D) systems, and Markovian jump repeated scalar nonlinear systems. Some sufficient conditions are first established respectively for the stability and performances of those kinds of stochastic jump hybrid systems in terms of solution of linear matrix inequalities (LMIs). Based on the derived analysis conditions, the filtering and control problems are addressed. The book presents up-to-date research developments and novel methodologies on stochastic jump hybrid systems. The contents can be divided into two parts: the first part is focused on robust filter design problem, while the second part is put the emphasis on robust control problem. These methodologies provide a framework for stability and performance analy...

Estimation of stochastic effects risk in children from areas affected by the Chernobyl accident

International Nuclear Information System (INIS)

Jova S, L.; Garcia L, O.; Valdes R, M.

1996-01-01

Radiation risk estimation of stochastic effect was evaluated in a group of children assisted in the Cuba Republic as part of the program for medical attention with children from areas affected by the Chernobyl accident . Doses, received from different sources, were estimated for risk evaluation. The study shows total detrimental effects between 0,02 - 0,01% for different groups; values lower than expected for developed country (17-20%). Fatal thyroid cancer increased up to 0,07% in one of the studied groups. (authors). 8 refs., 4 tabs

Estimation and variable selection for generalized additive partial linear models

KAUST Repository

Wang, Li

2011-08-01

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.

Estimation of non-linear continuous time models for the heat exchange dynamics of building integrated photovoltaic modules

DEFF Research Database (Denmark)

Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.

2008-01-01

This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiati...... that a description of the non-linear heat transfer is essential. The resulting model is a non-linear first order stochastic differential equation for the heat transfer of the PV component....... heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated facades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered...

Error Estimation for the Linearized Auto-Localization Algorithm

Directory of Open Access Journals (Sweden)

Fernando Seco

2012-02-01

Full Text Available The Linearized Auto-Localization (LAL algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs, using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons’ positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL, the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.

Simulation and inference for stochastic processes with YUIMA a comprehensive R framework for SDEs and other stochastic processes

CERN Document Server

Iacus, Stefano M

2018-01-01

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these ...

The multivariate supOU stochastic volatility model

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole; Stelzer, Robert

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order...... structure of the volatility, the log returns, as well as their "squares" are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations....... In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach....

Quantum stochastic calculus associated with quadratic quantum noises

International Nuclear Information System (INIS)

Ji, Un Cig; Sinha, Kalyan B.

2016-01-01

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus

Quantum stochastic calculus associated with quadratic quantum noises

Energy Technology Data Exchange (ETDEWEB)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods

KAUST Repository

Beck, Joakim; Tempone, Raul; Nobile, Fabio; Tamellini, Lorenzo

2012-01-01

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.

On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods

KAUST Repository

Beck, Joakim

2012-09-01

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.

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)

Stochastic resonance in models of neuronal ensembles

International Nuclear Information System (INIS)

Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.

1997-01-01

Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society

Electron heat transport in stochastic magnetic layer

International Nuclear Information System (INIS)

Becoulet, M.; Ghendrih, Ph.; Capes, H.; Grosman, A.

1999-06-01

Progress in the theoretical understanding of the local behaviour of the temperature field in ergodic layer was done in the framework of quasi-linear approach but this quasi-linear theory was not complete since the resonant modes coupling (due to stochasticity) was neglected. The stochastic properties of the magnetic field in the ergodic zone are now taken into account by a non-linear coupling of the temperature modes. The three-dimension heat transfer modelling in the ergodic-divertor configuration is performed by quasi-linear (ERGOT1) and non-linear (ERGOT2) numerical codes. The formalism and theoretical basis of both codes are presented. The most important effect that can be simulated with non-linear code is the averaged temperature profile flattening that occurs in the ergodic zone and the barrier creation that appears near the separatrix during divertor operation. (A.C.)

Linear System Control Using Stochastic Learning Automata

Science.gov (United States)

Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.

1998-01-01

This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.

PC analysis of stochastic differential equations driven by Wiener noise

KAUST Repository

Le Maitre, Olivier

2015-03-01

A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.

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...

Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis

Science.gov (United States)

Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel

2013-01-01

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007

Rare event simulation for stochastic fixed point equations related to the smoothing transform

DEFF Research Database (Denmark)

Collamore, Jeffrey F.; Vidyashankar, Anand N.; Xu, Jie

2013-01-01

In several applications arising in computer science, cascade theory, and other applied areas, it is of interest to evaluate the tail probabilities of non-homogeneous stochastic fixed point equations. Recently, techniques have been developed for the related linear recursions, yielding tail estimates...... and importance sampling methods for these recursions. However, such methods do not routinely generalize to non-homogeneous recursions. Drawing on techniques from the weighted branching process literature, we present a consistent, strongly efficient importance sampling algorithm for estimating the tail...

A comparative study of the performances of some estimators of ...

African Journals Online (AJOL)

In linear regression model, regressors are assumed fixed in repeated sampling. ... error terms when normally distributed regressors are fixed (non – stochastic) with ... of the estimated parameter of the model at different levels of autocorrelation ...

State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems

DEFF Research Database (Denmark)

Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer Moesgaard

2016-01-01

problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter......State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible...

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.

Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model

International Nuclear Information System (INIS)

Kuosmanen, Timo

2012-01-01

Electricity distribution network is a prime example of a natural local monopoly. In many countries, electricity distribution is regulated by the government. Many regulators apply frontier estimation techniques such as data envelopment analysis (DEA) or stochastic frontier analysis (SFA) as an integral part of their regulatory framework. While more advanced methods that combine nonparametric frontier with stochastic error term are known in the literature, in practice, regulators continue to apply simplistic methods. This paper reports the main results of the project commissioned by the Finnish regulator for further development of the cost frontier estimation in their regulatory framework. The key objectives of the project were to integrate a stochastic SFA-style noise term to the nonparametric, axiomatic DEA-style cost frontier, and to take the heterogeneity of firms and their operating environments better into account. To achieve these objectives, a new method called stochastic nonparametric envelopment of data (StoNED) was examined. Based on the insights and experiences gained in the empirical analysis using the real data of the regulated networks, the Finnish regulator adopted the StoNED method in use from 2012 onwards.

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

Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

KAUST Repository

Jaleel, Hassan; Shamma, Jeff S.

2018-01-01

dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through

Stochastic Subspace Modelling of Turbulence

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.

2009-01-01

positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order......, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.......Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...

Oriented stochastic data envelopment models: ranking comparison to stochastic frontier approach

Czech Academy of Sciences Publication Activity Database

Brázdik, František

-, č. 271 (2005), s. 1-46 ISSN 1211-3298 Institutional research plan: CEZ:AV0Z70850503 Keywords : stochastic data envelopment analysis * linear programming * rice farm Subject RIV: AH - Economics http://www.cerge-ei.cz/pdf/wp/Wp271.pdf

Estimation of group means when adjusting for covariates in generalized linear models.

Science.gov (United States)

Qu, Yongming; Luo, Junxiang

2015-01-01

Generalized linear models are commonly used to analyze categorical data such as binary, count, and ordinal outcomes. Adjusting for important prognostic factors or baseline covariates in generalized linear models may improve the estimation efficiency. The model-based mean for a treatment group produced by most software packages estimates the response at the mean covariate, not the mean response for this treatment group for the studied population. Although this is not an issue for linear models, the model-based group mean estimates in generalized linear models could be seriously biased for the true group means. We propose a new method to estimate the group mean consistently with the corresponding variance estimation. Simulation showed the proposed method produces an unbiased estimator for the group means and provided the correct coverage probability. The proposed method was applied to analyze hypoglycemia data from clinical trials in diabetes. Copyright © 2014 John Wiley & Sons, Ltd.

Presentation of a stochastic model estimating the wind energy contribution in remote island electrical networks

International Nuclear Information System (INIS)

Kaldellis, J.K.; Kapsali, M.; Tiligadas, D.

2012-01-01

Highlights: ► This study estimates the maximum wind energy contribution to an isolated micro-grid. ► An integrated computational tool is developed on the basis of stochastic analysis. ► The probability distribution of the wind energy surplus and deficit is estimated. ► The results indicate that a strict penetration limit is imposed to wind energy. -- Abstract: The electrification in remote islands whose electricity distribution network is not connected to the mainland’s grid is mostly based on Autonomous Power Stations (APSs) that are usually characterized by a considerably high electricity production cost, while at the same time the contribution of Renewable Energy Sources (RES) in these regions accounts for less than 10% of the total electricity generation. This actually results from the fact that despite the excellent wind potential of most of these islands, the wind energy contribution is significantly restricted from limits imposed to protect the remote electrical grids from possible instability problems, due to the stochastic wind speed behavior and the variable electricity consumption. On the basis of probability distribution of the load demand of a representative Greek island and the corresponding data related to the available wind potential, the present study estimates the maximum – acceptable by the local grid – wind energy contribution. For that reason, an integrated computational algorithm has been developed from first principles, based on a stochastic analysis. According to the results obtained, it becomes evident that with the current wind turbine technology, wind energy cannot play a key role in coping with the electrification problems encountered in many Greek island regions, excluding however the case of introducing bulk energy storage systems that may provide considerable recovery of the remarkable wind energy rejections expected.

A probabilistic graphical model based stochastic input model construction

International Nuclear Information System (INIS)

Wan, Jiang; Zabaras, Nicholas

2014-01-01

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media

Thresholding projection estimators in functional linear models

OpenAIRE

Cardot, Hervé; Johannes, Jan

2010-01-01

We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squ...

Multivariate moment closure techniques for stochastic kinetic models

International Nuclear Information System (INIS)

Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.

2015-01-01

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs

Multivariate moment closure techniques for stochastic kinetic models

Energy Technology Data Exchange (ETDEWEB)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

KAUST Repository

Almeida, Regina C.

2010-08-01

A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

International Nuclear Information System (INIS)

Hua-Guang, Zhang; Tie-Dong, Ma; Jie, Fu; Shao-Cheng, Tong

2009-01-01

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

KAUST Repository

Almeida, Regina C.; Oden, J. Tinsley

2010-01-01

A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.

Accurate and quantitative polarization-sensitive OCT by unbiased birefringence estimator with noise-stochastic correction

Science.gov (United States)

Kasaragod, Deepa; Sugiyama, Satoshi; Ikuno, Yasushi; Alonso-Caneiro, David; Yamanari, Masahiro; Fukuda, Shinichi; Oshika, Tetsuro; Hong, Young-Joo; Li, En; Makita, Shuichi; Miura, Masahiro; Yasuno, Yoshiaki

2016-03-01

Polarization sensitive optical coherence tomography (PS-OCT) is a functional extension of OCT that contrasts the polarization properties of tissues. It has been applied to ophthalmology, cardiology, etc. Proper quantitative imaging is required for a widespread clinical utility. However, the conventional method of averaging to improve the signal to noise ratio (SNR) and the contrast of the phase retardation (or birefringence) images introduce a noise bias offset from the true value. This bias reduces the effectiveness of birefringence contrast for a quantitative study. Although coherent averaging of Jones matrix tomography has been widely utilized and has improved the image quality, the fundamental limitation of nonlinear dependency of phase retardation and birefringence to the SNR was not overcome. So the birefringence obtained by PS-OCT was still not accurate for a quantitative imaging. The nonlinear effect of SNR to phase retardation and birefringence measurement was previously formulated in detail for a Jones matrix OCT (JM-OCT) [1]. Based on this, we had developed a maximum a-posteriori (MAP) estimator and quantitative birefringence imaging was demonstrated [2]. However, this first version of estimator had a theoretical shortcoming. It did not take into account the stochastic nature of SNR of OCT signal. In this paper, we present an improved version of the MAP estimator which takes into account the stochastic property of SNR. This estimator uses a probability distribution function (PDF) of true local retardation, which is proportional to birefringence, under a specific set of measurements of the birefringence and SNR. The PDF was pre-computed by a Monte-Carlo (MC) simulation based on the mathematical model of JM-OCT before the measurement. A comparison between this new MAP estimator, our previous MAP estimator [2], and the standard mean estimator is presented. The comparisons are performed both by numerical simulation and in vivo measurements of anterior and

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids.

Science.gov (United States)

Ali, S M; Mehmood, C A; Khan, B; Jawad, M; Farid, U; Jadoon, J K; Ali, M; Tareen, N K; Usman, S; Majid, M; Anwar, S M

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.

Remaining useful life estimation based on stochastic deterioration models: A comparative study

International Nuclear Information System (INIS)

Le Son, Khanh; Fouladirad, Mitra; Barros, Anne; Levrat, Eric; Iung, Benoît

2013-01-01

Prognostic of system lifetime is a basic requirement for condition-based maintenance in many application domains where safety, reliability, and availability are considered of first importance. This paper presents a probabilistic method for prognostic applied to the 2008 PHM Conference Challenge data. A stochastic process (Wiener process) combined with a data analysis method (Principal Component Analysis) is proposed to model the deterioration of the components and to estimate the RUL on a case study. The advantages of our probabilistic approach are pointed out and a comparison with existing results on the same data is made

Linear minimax estimation for random vectors with parametric uncertainty

KAUST Repository

Bitar, E

2010-06-01

In this paper, we take a minimax approach to the problem of computing a worst-case linear mean squared error (MSE) estimate of X given Y , where X and Y are jointly distributed random vectors with parametric uncertainty in their distribution. We consider two uncertainty models, PA and PB. Model PA represents X and Y as jointly Gaussian whose covariance matrix Λ belongs to the convex hull of a set of m known covariance matrices. Model PB characterizes X and Y as jointly distributed according to a Gaussian mixture model with m known zero-mean components, but unknown component weights. We show: (a) the linear minimax estimator computed under model PA is identical to that computed under model PB when the vertices of the uncertain covariance set in PA are the same as the component covariances in model PB, and (b) the problem of computing the linear minimax estimator under either model reduces to a semidefinite program (SDP). We also consider the dynamic situation where x(t) and y(t) evolve according to a discrete-time LTI state space model driven by white noise, the statistics of which is modeled by PA and PB as before. We derive a recursive linear minimax filter for x(t) given y(t).

On the stochastic stability of MHD equilibria

International Nuclear Information System (INIS)

Teichmann, J.

1979-07-01

The stochastic stability in the large of stationary equilibria of ideal and dissipative magnetohydrodynamics under the influence of stationary random fluctuations is studied using the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian systems are given. The destabilizing effect of stochastic fluctuations is demonstrated. (orig.)

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

Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss

Directory of Open Access Journals (Sweden)

Yingqi Zhang

2012-01-01

Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.

Tail estimates for stochastic fixed point equations via nonlinear renewal theory

DEFF Research Database (Denmark)

Collamore, Jeffrey F.; Vidyashankar, Anand N.

2013-01-01

estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....

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

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

Science.gov (United States)

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

KAUST Repository

Schillinger, Dominik

2013-07-01

The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed. © 2013 Elsevier Ltd.

Optimal Stochastic Modeling and Control of Flexible Structures

Science.gov (United States)

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Biological Inspired Stochastic Optimization Technique (PSO for DOA and Amplitude Estimation of Antenna Arrays Signal Processing in RADAR Communication System

Directory of Open Access Journals (Sweden)

Khurram Hammed

2016-01-01

Full Text Available This paper presents a stochastic global optimization technique known as Particle Swarm Optimization (PSO for joint estimation of amplitude and direction of arrival of the targets in RADAR communication system. The proposed scheme is an excellent optimization methodology and a promising approach for solving the DOA problems in communication systems. Moreover, PSO is quite suitable for real time scenario and easy to implement in hardware. In this study, uniform linear array is used and targets are supposed to be in far field of the arrays. Formulation of the fitness function is based on mean square error and this function requires a single snapshot to obtain the best possible solution. To check the accuracy of the algorithm, all of the results are taken by varying the number of antenna elements and targets. Finally, these results are compared with existing heuristic techniques to show the accuracy of PSO.

LP formulation of asymmetric zero-sum stochastic games

KAUST Repository

Li, Lichun

2014-12-15

This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of the state at each stage, and the transition law is only controlled by the informed player. Compared with the LP formulation of extensive stochastic games whose size grows polynomially with respect to the size of the state and the size of the uninformed player\\'s actions, our proposed LP formulation has its size to be linear with respect to the size of the state and the size of the uninformed player, and hence greatly reduces the computational complexity. A travelling inspector problem is used to demonstrate the efficiency of the proposed LP formulation.

LP formulation of asymmetric zero-sum stochastic games

KAUST Repository

Li, Lichun; Shamma, Jeff S.

2014-01-01

This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of the state at each stage, and the transition law is only controlled by the informed player. Compared with the LP formulation of extensive stochastic games whose size grows polynomially with respect to the size of the state and the size of the uninformed player's actions, our proposed LP formulation has its size to be linear with respect to the size of the state and the size of the uninformed player, and hence greatly reduces the computational complexity. A travelling inspector problem is used to demonstrate the efficiency of the proposed LP formulation.

Robust linear discriminant analysis with distance based estimators

Science.gov (United States)

Lim, Yai-Fung; Yahaya, Sharipah Soaad Syed; Ali, Hazlina

2017-11-01

Linear discriminant analysis (LDA) is one of the supervised classification techniques concerning relationship between a categorical variable and a set of continuous variables. The main objective of LDA is to create a function to distinguish between populations and allocating future observations to previously defined populations. Under the assumptions of normality and homoscedasticity, the LDA yields optimal linear discriminant rule (LDR) between two or more groups. However, the optimality of LDA highly relies on the sample mean and pooled sample covariance matrix which are known to be sensitive to outliers. To alleviate these conflicts, a new robust LDA using distance based estimators known as minimum variance vector (MVV) has been proposed in this study. The MVV estimators were used to substitute the classical sample mean and classical sample covariance to form a robust linear discriminant rule (RLDR). Simulation and real data study were conducted to examine on the performance of the proposed RLDR measured in terms of misclassification error rates. The computational result showed that the proposed RLDR is better than the classical LDR and was comparable with the existing robust LDR.

Characterization of flood and precipitation events in Southwestern Germany and stochastic simulation of extreme precipitation (Project FLORIS-SV)

Science.gov (United States)

Florian, Ehmele; Michael, Kunz

2016-04-01

Several major flood events occurred in Germany in the past 15-20 years especially in the eastern parts along the rivers Elbe and Danube. Examples include the major floods of 2002 and 2013 with an estimated loss of about 2 billion Euros each. The last major flood events in the State of Baden-Württemberg in southwest Germany occurred in the years 1978 and 1993/1994 along the rivers Rhine and Neckar with an estimated total loss of about 150 million Euros (converted) each. Flood hazard originates from a combination of different meteorological, hydrological and hydraulic processes. Currently there is no defined methodology available for evaluating and quantifying the flood hazard and related risk for larger areas or whole river catchments instead of single gauges. In order to estimate the probable maximum loss for higher return periods (e.g. 200 years, PML200), a stochastic model approach is designed since observational data are limited in time and space. In our approach, precipitation is linearly composed of three elements: background precipitation, orographically-induces precipitation, and a convectively-driven part. We use linear theory of orographic precipitation formation for the stochastic precipitation model (SPM), which is based on fundamental statistics of relevant atmospheric variables. For an adequate number of historic flood events, the corresponding atmospheric conditions and parameters are determined in order to calculate a probability density function (pdf) for each variable. This method involves all theoretically possible scenarios which may not have happened, yet. This work is part of the FLORIS-SV (FLOod RISk Sparkassen Versicherung) project and establishes the first step of a complete modelling chain of the flood risk. On the basis of the generated stochastic precipitation event set, hydrological and hydraulic simulations will be performed to estimate discharge and water level. The resulting stochastic flood event set will be used to quantify the

Performances of estimators of linear auto-correlated error model ...

African Journals Online (AJOL)

The performances of five estimators of linear models with autocorrelated disturbance terms are compared when the independent variable is exponential. The results reveal that for both small and large samples, the Ordinary Least Squares (OLS) compares favourably with the Generalized least Squares (GLS) estimators in ...

Stochastic linear dynamical programming in order to apply it in energy modelling

Energy Technology Data Exchange (ETDEWEB)

El Hachem, S

1995-11-01

This thesis contributes to the development of new algorithms for the computation of stochastic dynamic problem and its mini-maxi variant for the case of imperfect knowledge on random data. The proposed algorithms are scenarios aggregation type. It also contributes to integrate these algorithms in a decision support approach and to discuss the stochastic modeling of two energy problems: the refining and the portfolio gas contracts. (author). 112 refs., 5 tabs.

Bounded Perturbation Regularization for Linear Least Squares Estimation

KAUST Repository

Ballal, Tarig; Suliman, Mohamed Abdalla Elhag; Al-Naffouri, Tareq Y.

2017-01-01

This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded

M-estimator for the 3D symmetric Helmert coordinate transformation

Science.gov (United States)

Chang, Guobin; Xu, Tianhe; Wang, Qianxin

2018-01-01

The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3 × 1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method's statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not.

Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks

Directory of Open Access Journals (Sweden)

Charalambous Charalambos D

2006-01-01

Full Text Available A new time-varying (TV long-term fading (LTF channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.

Common Nearly Best Linear Estimates of Location and Scale ...

African Journals Online (AJOL)

Common nearly best linear estimates of location and scale parameters of normal and logistic distributions, which are based on complete samples, are considered. Here, the population from which the samples are drawn is either normal or logistic population or a fusion of both distributions and the estimates are computed ...

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

Directory of Open Access Journals (Sweden)

MC. Souza

Full Text Available Leaf area estimation is an important biometrical trait for evaluating leaf development and plant growth in field and pot experiments. We developed a non-destructive model to estimate the leaf area (LA of Vernonia ferruginea using the length (L and width (W leaf dimensions. Different combinations of linear equations were obtained from L, L2, W, W2, LW and L2W2. The linear regressions using the product of LW dimensions were more efficient to estimate the LA of V. ferruginea than models based on a single dimension (L, W, L2 or W2. Therefore, the linear regression “LA=0.463+0.676WL” provided the most accurate estimate of V. ferruginea leaf area. Validation of the selected model showed that the correlation between real measured leaf area and estimated leaf area was very high.

Stochastic fusion of dynamic hydrological and geophysical data for estimating hydraulic conductivities: insights and observations (Invited)

Science.gov (United States)

Irving, J. D.; Singha, K.

2010-12-01

Traditionally, hydrological measurements have been used to estimate subsurface properties controlling groundwater flow and contaminant transport. However, such measurements are limited by their support volume and expense. A considerable benefit of geophysical measurements is that they provide a degree of spatial coverage and resolution that are unattainable with other methods, and the data can be acquired in a cost-effective manner. In particular, dynamic geophysical data allow us to indirectly observe changes in hydrological state variables as flow and transport processes occur, and can thus provide a link to hydrological properties when coupled with a process-based model. Stochastic fusion of these two data types offers the potential to provide not only estimates of subsurface hydrological properties, but also a quantification of their uncertainty. This information is critical when considering the end use of the data, which may be for groundwater remediation and management decision making. Here, we examine a number of key issues in the stochastic fusion of dynamic hydrogeophysical data. We focus our attention on the specific problem of integrating time-lapse crosshole electrical resistivity measurements and saline tracer-test concentration data in order to estimate the spatial distribution of hydraulic conductivity (K). To assimilate the geophysical and hydrological measurements in a stochastic manner, we use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology. This provides multiple realizations of the subsurface K field that are consistent with the measured data and assumptions regarding model structure and data errors. To account for incomplete petrophysical knowledge, the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration following the general form of Archie’s law. To make the spatially distributed, fully stochastic inverse problem computationally tractable, we take

Infinite stochastic acceleration of charged particles from non-relativistic initial energies

International Nuclear Information System (INIS)

Buts, V.A.; Manujlenko, O.V.; Turkin, Yu.A.

1997-01-01

Stochastic charged particle acceleration by electro-magnetic field due to overlapping of non-linear cyclotron resonances is considered. It was shown that non-relativistic charged particles are involved in infinitive stochastic acceleration regime. This effect can be used for stochastic acceleration or for plasma heating by regular electro-magnetic fields

Stochastic precision analysis of 2D cardiac strain estimation in vivo

International Nuclear Information System (INIS)

Bunting, E A; Provost, J; Konofagou, E E

2014-01-01

Ultrasonic strain imaging has been applied to echocardiography and carries great potential to be used as a tool in the clinical setting. Two-dimensional (2D) strain estimation may be useful when studying the heart due to the complex, 3D deformation of the cardiac tissue. Increasing the framerate used for motion estimation, i.e. motion estimation rate (MER), has been shown to improve the precision of the strain estimation, although maintaining the spatial resolution necessary to view the entire heart structure in a single heartbeat remains challenging at high MERs. Two previously developed methods, the temporally unequispaced acquisition sequence (TUAS) and the diverging beam sequence (DBS), have been used in the past to successfully estimate in vivo axial strain at high MERs without compromising spatial resolution. In this study, a stochastic assessment of 2D strain estimation precision is performed in vivo for both sequences at varying MERs (65, 272, 544, 815 Hz for TUAS; 250, 500, 1000, 2000 Hz for DBS). 2D incremental strains were estimated during left ventricular contraction in five healthy volunteers using a normalized cross-correlation function and a least-squares strain estimator. Both sequences were shown capable of estimating 2D incremental strains in vivo. The conditional expected value of the elastographic signal-to-noise ratio (E(SNRe|ε)) was used to compare strain estimation precision of both sequences at multiple MERs over a wide range of clinical strain values. The results here indicate that axial strain estimation precision is much more dependent on MER than lateral strain estimation, while lateral estimation is more affected by strain magnitude. MER should be increased at least above 544 Hz to avoid suboptimal axial strain estimation. Radial and circumferential strain estimations were influenced by the axial and lateral strain in different ways. Furthermore, the TUAS and DBS were found to be of comparable precision at similar MERs. (paper)

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

International Nuclear Information System (INIS)

Desai, Ajit; Pettit, Chris; Poirel, Dominique; Sarkar, Abhijit

2017-01-01

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

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)

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).

Stochastic estimation approach for the evaluation of thermal-hydraulic parameters in pressurized water reactors

International Nuclear Information System (INIS)

Shieh, D.J.; Upadhyaya, M.G.

1986-01-01

A method based on the extended Kalman filter is developed for the estimation of the core coolant mass flow rate in pressurized water reactors. The need for flow calibration can be avoided by a direct estimation of this parameter. A reduced-order neutronic and thermal-hydraulic model is developed for the Loss-of-Fluid Test (LOFT) reactor. The neutron detector and core-exit coolant temperature signals from the LOFT reactor are used as measurements in the parameter estimation algorithm. The estimation sensitivity to model uncertainties was evaluated using the ambiguity function analysis. This also provides a lower bound on the measurement sample size necessary to achieve a certain estimation accuracy. A sequential technique was developed to minimize the computational effort needed to discretize the continuous time equations, and thus achieve faster convergence to the true parameter value. The performance of the stochastic approximation method was first evaluated using simulated random data, and then applied to the estimation of coolant flow rate using the operational data from the LOFT reactor at 100 and 65% flow rate conditions

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.''

Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

DEFF Research Database (Denmark)

Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

1994-01-01

perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process

International Nuclear Information System (INIS)

Maslowski, Bohdan; Pospisil, Jan

2008-01-01

Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise

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...

Linear response in stochastic mean-field theories and the onset of instabilities

International Nuclear Information System (INIS)

Colonna, M.; Chomaz, Ph.

1993-01-01

The small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach is studied. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions. (author) 14 refs.; 5 figs

The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

KAUST Repository

Schillinger, Dominik; Stefanov, Dimitar; Stavrev, Atanas

2013-01-01

-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed

Variance estimation for complex indicators of poverty and inequality using linearization techniques

Directory of Open Access Journals (Sweden)

Guillaume Osier

2009-12-01

Full Text Available The paper presents the Eurostat experience in calculating measures of precision, including standard errors, confidence intervals and design effect coefficients - the ratio of the variance of a statistic with the actual sample design to the variance of that statistic with a simple random sample of same size - for the "Laeken" indicators, that is, a set of complex indicators of poverty and inequality which had been set out in the framework of the EU-SILC project (European Statistics on Income and Living Conditions. The Taylor linearization method (Tepping, 1968; Woodruff, 1971; Wolter, 1985; Tille, 2000 is actually a well-established method to obtain variance estimators for nonlinear statistics such as ratios, correlation or regression coefficients. It consists of approximating a nonlinear statistic with a linear function of the observations by using first-order Taylor Series expansions. Then, an easily found variance estimator of the linear approximation is used as an estimator of the variance of the nonlinear statistic. Although the Taylor linearization method handles all the nonlinear statistics which can be expressed as a smooth function of estimated totals, the approach fails to encompass the "Laeken" indicators since the latter are having more complex mathematical expressions. Consequently, a generalized linearization method (Deville, 1999, which relies on the concept of influence function (Hampel, Ronchetti, Rousseeuw and Stahel, 1986, has been implemented. After presenting the EU-SILC instrument and the main target indicators for which variance estimates are needed, the paper elaborates on the main features of the linearization approach based on influence functions. Ultimately, estimated standard errors, confidence intervals and design effect coefficients obtained from this approach are presented and discussed.

Kalman filtering state of charge estimation for battery management system based on a stochastic fuzzy neural network battery model

International Nuclear Information System (INIS)

Xu Long; Wang Junping; Chen Quanshi

2012-01-01

Highlights: ► A novel extended Kalman Filtering SOC estimation method based on a stochastic fuzzy neural network (SFNN) battery model is proposed. ► The SFNN which has filtering effect on noisy input can model the battery nonlinear dynamic with high accuracy. ► A robust parameter learning algorithm for SFNN is studied so that the parameters can converge to its true value with noisy data. ► The maximum SOC estimation error based on the proposed method is 0.6%. - Abstract: Extended Kalman filtering is an intelligent and optimal means for estimating the state of a dynamic system. In order to use extended Kalman filtering to estimate the state of charge (SOC), we require a mathematical model that can accurately capture the dynamics of battery pack. In this paper, we propose a stochastic fuzzy neural network (SFNN) instead of the traditional neural network that has filtering effect on noisy input to model the battery nonlinear dynamic. Then, the paper studies the extended Kalman filtering SOC estimation method based on a SFNN model. The modeling test is realized on an 80 Ah Ni/MH battery pack and the Federal Urban Driving Schedule (FUDS) cycle is used to verify the SOC estimation method. The maximum SOC estimation error is 0.6% compared with the real SOC obtained from the discharging test.

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

Directory of Open Access Journals (Sweden)

Jae Sang Moon

2017-12-01

Full Text Available Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES. Stochastic characteristics of these LES waked wind velocity field, including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study’s overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

Science.gov (United States)

Mahdi Alavi, S. M.; Saif, Mehrdad

2013-12-01

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

Linear stochastic evaluation of tyre vibration due to tyre/road excitation

Science.gov (United States)

Rustighi, E.; Elliott, S. J.; Finnveden, S.; Gulyás, K.; Mócsai, T.; Danti, M.

2008-03-01

Tyre/road interaction is recognised as the main source of interior and exterior noise for velocities over the 40 km/h. In this paper, a three-dimensional (3D) elemental approach has been adopted to predict the stochastic tyre vibration and hence the interior and exterior noise due to this kind of excitation. The road excitation has been modelled from the spectral density of a common road profile, supposing the road to be an isotropic surface. A linear Winkler bedding connects the 3D model of the tyre with the ground. The exterior noise has been evaluated by an elemental calculation of the radiation matrix of the tyre deformed by the static load on a concrete road. The noise inside the vehicle has also been calculated, using the transfer functions from the force transmitted to the hub and the noise inside the vehicle, which have been computed by a FEM model of a common car body. The simple formulation allows much quicker calculation than traditional nonlinear approaches, and appears to give results consistent with available measurements, although the effects of tyre rotation and of the nonlinearities in the contact model are yet to be quantified, and the method requires further experimental validation before practical application.

A stochastic model for the financial market with discontinuous prices

Directory of Open Access Journals (Sweden)

Leda D. Minkova

1996-01-01

Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.

Stochastic synchronization of coupled neural networks with intermittent control

International Nuclear Information System (INIS)

Yang Xinsong; Cao Jinde

2009-01-01

In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new results.

Stochastic Procedures for Extreme Wave Load Predictions- Wave Bending Moment in Ships

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2009-01-01

A discussion of useful stochastic procedures for stochastic wave load problems is given, covering the range from slightly linear to strongly non-linear (bifurcation) problems. The methods are: Hermite transformation, Critical wave episodes and the First Order Reliability Method (FORM). The proced......). The procedures will be illustrated by results for the extreme vertical wave bending moment in ships....

QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION

Directory of Open Access Journals (Sweden)

A.E.Kobryn

2003-01-01

Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

KAUST Repository

Jaleel, Hassan

2018-04-08

Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a framework for the comparative analysis of stochastic learning dynamics with different update rules but same steady-state behavior. We present the framework in the context of two learning dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through an example setup of sensor coverage game that for each of these dynamics, the paths to stochastically stable states exhibit distinctive behaviors. Therefore, we propose multiple criteria to analyze and quantify the differences in the short and medium run behavior of stochastic learning dynamics. We derive and compare upper bounds on the expected hitting time to the set of Nash equilibria for both LLL and ML. For the medium to long-run behavior, we identify a set of tools from the theory of perturbed Markov chains that result in a hierarchical decomposition of the state space into collections of states called cycles. We compare LLL and ML based on the proposed criteria and develop invaluable insights into the comparative behavior of the two dynamics.

Turbulent response in a stochastic regime

International Nuclear Information System (INIS)

Molvig, K.; Freidberg, J.P.; Potok, R.; Hirshman, S.P.; Whitson, J.C.; Tajima, T.

1981-06-01

The theory for the non-linear, turbulent response in a system with intrinsic stochasticity is considered. It is argued that perturbative Eulerian theories, such as the Direct Interaction Approximation (DIA), are inherently unsuited to describe such a system. The exponentiation property that characterizes stochasticity appears in the Lagrangian picture and cannot even be defined in the Eulerian representation. An approximation for stochastic systems - the Normal Stochastic Approximation - is developed and states that the perturbed orbit functions (Lagrangian fluctuations) behave as normally distributed random variables. This is independent of the Eulerian statistics and, in fact, we treat the Eulerian fluctuations as fixed. A simple model problem (appropriate for the electron response in the drift wave) is subjected to a series of computer experiments. To within numerical noise the results are in agreement with the Normal Stochastic Approximation. The predictions of the DIA for this mode show substantial qualitative and quantitative departures from the observations

Real-time prediction of extreme ambient carbon monoxide concentrations due to vehicular exhaust emissions using univariate linear stochastic models

International Nuclear Information System (INIS)

Sharma, P.; Khare, M.

2000-01-01

Historical data of the time-series of carbon monoxide (CO) concentration was analysed using Box-Jenkins modelling approach. Univariate Linear Stochastic Models (ULSMs) were developed to examine the degree of prediction possible for situations where only a limited data set, restricted only to the past record of pollutant data are available. The developed models can be used to provide short-term, real-time forecast of extreme CO concentrations for an Air Quality Control Region (AQCR), comprising a major traffic intersection in a Central Business District of Delhi City, India. (author)

A Hierarchical Linear Model for Estimating Gender-Based Earnings Differentials.

Science.gov (United States)

Haberfield, Yitchak; Semyonov, Moshe; Addi, Audrey

1998-01-01

Estimates of gender earnings inequality in data from 116,431 Jewish workers were compared using a hierarchical linear model (HLM) and ordinary least squares model. The HLM allows estimation of the extent to which earnings inequality depends on occupational characteristics. (SK)

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

KAUST Repository

Beck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2014-01-01

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

KAUST Repository

Beck, Joakim

2014-03-01

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.

A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models

Czech Academy of Sciences Publication Activity Database

Lánský, Petr; Ditlevsen, S.

2008-01-01

Roč. 99, 4-5 (2008), s. 253-262 ISSN 0340-1200 R&D Projects: GA MŠk(CZ) LC554; GA AV ČR(CZ) 1ET400110401 Institutional research plan: CEZ:AV0Z50110509 Keywords : parameter estimation * stochastic diffusion neuronal model Subject RIV: BO - Biophysics Impact factor: 1.935, year: 2008

Expressing stochastic unravellings using random evolution operators

International Nuclear Information System (INIS)

Salgado, D; Sanchez-Gomez, J L

2002-01-01

We prove how the form of the most general invariant stochastic unravelling for Markovian (recently given in the literature by Wiseman and Diosi) and non-Markovian but Lindblad-type open quantum systems can be attained by imposing a single mathematical condition upon the random evolution operator of the system, namely a.s. trace preservation (a.s. stands for almost surely). The use of random operators ensures the complete positivity of the density operator evolution and characterizes the linear/non-linear character of the evolution in a straightforward way. It is also shown how three quantum stochastic evolution models - continuous spontaneous localization, quantum state diffusion and quantum mechanics with universal position localization - appear as concrete choices for the noise term of the evolution random operators are assumed. We finally conjecture how these operators may in the future be used in two different directions: both to connect quantum stochastic evolution models with random properties of space-time and to handle noisy quantum logical gates

MEASURING INFLATION THROUGH STOCHASTIC APPROACH TO INDEX NUMBERS FOR PAKISTAN

Directory of Open Access Journals (Sweden)

Zahid Asghar

2010-09-01

Full Text Available This study attempts to estimate the rate of inflation in Pakistan through stochastic approach to index numbers which provides not only point estimate but also confidence interval for the rate of inflation. There are two types of approaches to index number theory namely: the functional economic approaches and the stochastic approach. The attraction of stochastic approach is that it estimates the rate of inflation in which uncertainty and statistical ideas play a major roll of screening index numbers. We have used extended stochastic approach to index numbers for measuring inflation by allowing for the systematic changes in the relative prices. We use CPI data covering the period July 2001--March 2008 for Pakistan.

A combined stochastic programming and optimal control approach to personal finance and pensions

DEFF Research Database (Denmark)

Konicz, Agnieszka Karolina; Pisinger, David; Rasmussen, Kourosh Marjani

2015-01-01

The paper presents a model that combines a dynamic programming (stochastic optimal control) approach and a multi-stage stochastic linear programming approach (SLP), integrated into one SLP formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement....

Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

Directory of Open Access Journals (Sweden)

Giorgos Minas

2017-07-01

Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

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.

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

Stochastic models and reliability parameter estimation applicable to nuclear power plant safety

International Nuclear Information System (INIS)

Mitra, S.P.

1979-01-01

A set of stochastic models and related estimation schemes for reliability parameters are developed. The models are applicable for evaluating reliability of nuclear power plant systems. Reliability information is extracted from model parameters which are estimated from the type and nature of failure data that is generally available or could be compiled in nuclear power plants. Principally, two aspects of nuclear power plant reliability have been investigated: (1) The statistical treatment of inplant component and system failure data; (2) The analysis and evaluation of common mode failures. The model inputs are failure data which have been classified as either the time type of failure data or the demand type of failure data. Failures of components and systems in nuclear power plant are, in general, rare events.This gives rise to sparse failure data. Estimation schemes for treating sparse data, whenever necessary, have been considered. The following five problems have been studied: 1) Distribution of sparse failure rate component data. 2) Failure rate inference and reliability prediction from time type of failure data. 3) Analyses of demand type of failure data. 4) Common mode failure model applicable to time type of failure data. 5) Estimation of common mode failures from 'near-miss' demand type of failure data

Cross sectional efficient estimation of stochastic volatility short rate models

NARCIS (Netherlands)

Danilov, Dmitri; Mandal, Pranab K.

2002-01-01

We consider the problem of estimation of term structure of interest rates. Filtering theory approach is very natural here with the underlying setup being non-linear and non-Gaussian. Earlier works make use of Extended Kalman Filter (EKF). However, the EKF in this situation leads to inconsistent

Estimation of parameter sensitivities for stochastic reaction networks

KAUST Repository

Gupta, Ankit

2016-01-01

Quantification of the effects of parameter uncertainty is an important and challenging problem in Systems Biology. We consider this problem in the context of stochastic models of biochemical reaction networks where the dynamics is described as a

Maximum principle for a stochastic delayed system involving terminal state constraints.

Science.gov (United States)

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Parameter-free resolution of the superposition of stochastic signals

Energy Technology Data Exchange (ETDEWEB)

Scholz, Teresa, E-mail: tascholz@fc.ul.pt [Center for Theoretical and Computational Physics, University of Lisbon (Portugal); Raischel, Frank [Center for Geophysics, IDL, University of Lisbon (Portugal); Closer Consulting, Av. Eng. Duarte Pacheco Torre 1 15" 0, 1070-101 Lisboa (Portugal); Lopes, Vitor V. [DEIO-CIO, University of Lisbon (Portugal); UTEC–Universidad de Ingeniería y Tecnología, Lima (Peru); Lehle, Bernd; Wächter, Matthias; Peinke, Joachim [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Lind, Pedro G. [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Institute of Physics, University of Osnabrück, Osnabrück (Germany)

2017-01-30

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent stochastic processes, one of which is an Ornstein–Uhlenbeck process and the other a general (non-linear) Langevin process. The method is able to distinguish between the stochastic processes, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.

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 ...

Cross sectional efficient estimation of stochastic volatility short rate models

NARCIS (Netherlands)

Danilov, Dmitri; Mandal, Pranab K.

2001-01-01

We consider the problem of estimation of term structure of interest rates. Filtering theory approach is very natural here with the underlying setup being non-linear and non-Gaussian. Earlier works make use of Extended Kalman Filter (EKF). However, as indicated by de Jong (2000), the EKF in this

Portfolio management of hydropower producer via stochastic programming

International Nuclear Information System (INIS)

Liu, Hongling; Jiang, Chuanwen; Zhang, Yan

2009-01-01

This paper presents a stochastic linear programming framework for the hydropower portfolio management problem with uncertainty in market prices and inflows on medium term. The uncertainty is modeled as a scenario tree using the Monte Carlo simulation method, and the objective is to maximize the expected revenue over the entire scenario tree. The portfolio decisions of the stochastic model are formulated as a tradeoff involving different scenarios. Numerical results illustrate the impact of uncertainty on the portfolio management decisions, and indicate the significant value of stochastic solution. (author)

A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

Energy Technology Data Exchange (ETDEWEB)

Addona, Davide, E-mail: d.addona@campus.unimib.it [Università degli Studi di Milano Bicocca, (MILANO BICOCCA) Dipartimento di Matematica (Italy)

2015-08-15

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

Admissible Estimators in the General Multivariate Linear Model with Respect to Inequality Restricted Parameter Set

Directory of Open Access Journals (Sweden)

Shangli Zhang

2009-01-01

Full Text Available By using the methods of linear algebra and matrix inequality theory, we obtain the characterization of admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set. In the classes of homogeneous and general linear estimators, the necessary and suffcient conditions that the estimators of regression coeffcient function are admissible are established.

Robust-BD Estimation and Inference for General Partially Linear Models

Directory of Open Access Journals (Sweden)

Chunming Zhang

2017-11-01

Full Text Available The classical quadratic loss for the partially linear model (PLM and the likelihood function for the generalized PLM are not resistant to outliers. This inspires us to propose a class of “robust-Bregman divergence (BD” estimators of both the parametric and nonparametric components in the general partially linear model (GPLM, which allows the distribution of the response variable to be partially specified, without being fully known. Using the local-polynomial function estimation method, we propose a computationally-efficient procedure for obtaining “robust-BD” estimators and establish the consistency and asymptotic normality of the “robust-BD” estimator of the parametric component β o . For inference procedures of β o in the GPLM, we show that the Wald-type test statistic W n constructed from the “robust-BD” estimators is asymptotically distribution free under the null, whereas the likelihood ratio-type test statistic Λ n is not. This provides an insight into the distinction from the asymptotic equivalence (Fan and Huang 2005 between W n and Λ n in the PLM constructed from profile least-squares estimators using the non-robust quadratic loss. Numerical examples illustrate the computational effectiveness of the proposed “robust-BD” estimators and robust Wald-type test in the appearance of outlying observations.

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

Science.gov (United States)

Lin, Huiming; Fu, Bo; Qin, Guoyou; Zhu, Zhongyi

2017-12-01

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study. © 2017, The International Biometric Society.

Importance Sampling for Stochastic Timed Automata

DEFF Research Database (Denmark)

Jegourel, Cyrille; Larsen, Kim Guldstrand; Legay, Axel

2016-01-01

We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state-wise cha......We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state...

Fastest Rates for Stochastic Mirror Descent Methods

KAUST Repository

Hanzely, Filip; Richtarik, Peter

2018-01-01

Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.

Fastest Rates for Stochastic Mirror Descent Methods

KAUST Repository

Hanzely, Filip

2018-03-20

Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.

Stochastic differential equation model to Prendiville processes

International Nuclear Information System (INIS)

Granita; Bahar, Arifah

2015-01-01

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

Stochastic differential equation model to Prendiville processes

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

2015-10-22

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

Linear Estimation of Standard Deviation of Logistic Distribution ...

African Journals Online (AJOL)

The paper presents a theoretical method based on order statistics and a FORTRAN program for computing the variance and relative efficiencies of the standard deviation of the logistic population with respect to the Cramer-Rao lower variance bound and the best linear unbiased estimators (BLUE\\'s) when the mean is ...

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...

From spiking neuron models to linear-nonlinear models.

Science.gov (United States)

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

An Entropic Estimator for Linear Inverse Problems

Directory of Open Access Journals (Sweden)

Amos Golan

2012-05-01

Full Text Available In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists, and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

Science.gov (United States)

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

A Comparison of Alternative Estimators of Linearly Aggregated Macro Models

Directory of Open Access Journals (Sweden)

Fikri Akdeniz

2012-07-01

Full Text Available Normal 0 false false false TR X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Times New Roman","serif"; mso-ansi-language:TR; mso-fareast-language:TR;} This paper deals with the linear aggregation problem. For the true underlying micro relations, which explain the micro behavior of the individuals, no restrictive rank conditions are assumed. Thus the analysis is presented in a framework utilizing generalized inverses of singular matrices. We investigate several estimators for certain linear transformations of the systematic part of the corresponding macro relations. Homogeneity of micro parameters is discussed. Best linear unbiased estimation for micro parameters is described.

Weighted conditional least-squares estimation

International Nuclear Information System (INIS)

Booth, J.G.

1987-01-01

A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered

Sensitivity of Footbridge Vibrations to Stochastic Walking Parameters

DEFF Research Database (Denmark)

Pedersen, Lars; Frier, Christian

2010-01-01

of the pedestrian. A stochastic modelling approach is adopted for this paper and it facilitates quantifying the probability of exceeding various vibration levels, which is useful in a discussion of serviceability of a footbridge design. However, estimates of statistical distributions of footbridge vibration levels...... to walking loads might be influenced by the models assumed for the parameters of the load model (the walking parameters). The paper explores how sensitive estimates of the statistical distribution of vertical footbridge response are to various stochastic assumptions for the walking parameters. The basis...... for the study is a literature review identifying different suggestions as to how the stochastic nature of these parameters may be modelled, and a parameter study examines how the different models influence estimates of the statistical distribution of footbridge vibrations. By neglecting scatter in some...

Stochastically Estimating Modular Criticality in Large-Scale Logic Circuits Using Sparsity Regularization and Compressive Sensing

Directory of Open Access Journals (Sweden)

Mohammed Alawad

2015-03-01

Full Text Available This paper considers the problem of how to efficiently measure a large and complex information field with optimally few observations. Specifically, we investigate how to stochastically estimate modular criticality values in a large-scale digital circuit with a very limited number of measurements in order to minimize the total measurement efforts and time. We prove that, through sparsity-promoting transform domain regularization and by strategically integrating compressive sensing with Bayesian learning, more than 98% of the overall measurement accuracy can be achieved with fewer than 10% of measurements as required in a conventional approach that uses exhaustive measurements. Furthermore, we illustrate that the obtained criticality results can be utilized to selectively fortify large-scale digital circuits for operation with narrow voltage headrooms and in the presence of soft-errors rising at near threshold voltage levels, without excessive hardware overheads. Our numerical simulation results have shown that, by optimally allocating only 10% circuit redundancy, for some large-scale benchmark circuits, we can achieve more than a three-times reduction in its overall error probability, whereas if randomly distributing such 10% hardware resource, less than 2% improvements in the target circuit’s overall robustness will be observed. Finally, we conjecture that our proposed approach can be readily applied to estimate other essential properties of digital circuits that are critical to designing and analyzing them, such as the observability measure in reliability analysis and the path delay estimation in stochastic timing analysis. The only key requirement of our proposed methodology is that these global information fields exhibit a certain degree of smoothness, which is universally true for almost any physical phenomenon.

Stochastic search, optimization and regression with energy applications

Science.gov (United States)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

Energy Technology Data Exchange (ETDEWEB)

Thimmisetty, Charanraj A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zhao, Wenju [Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing; Chen, Xiao [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Tong, Charles H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; White, Joshua A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.

Lyapunov functionals and stability of stochastic functional differential equations

CERN Document Server

Shaikhet, Leonid

2013-01-01

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...

On estimation of the noise variance in high-dimensional linear models

OpenAIRE

Golubev, Yuri; Krymova, Ekaterina

2017-01-01

We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator. The noise estimation is based on the adaptive normalisation of the squared error. We derive the upper bound for the concentration of the proposed method around the ideal estimator (the case of zero nuisance).

Linear estimation of coherent structures in wall-bounded turbulence at Re τ = 2000

Science.gov (United States)

Oehler, S.; Garcia–Gutiérrez, A.; Illingworth, S.

2018-04-01

The estimation problem for a fully-developed turbulent channel flow at Re τ = 2000 is considered. Specifically, a Kalman filter is designed using a Navier–Stokes-based linear model. The estimator uses time-resolved velocity measurements at a single wall-normal location (provided by DNS) to estimate the time-resolved velocity field at other wall-normal locations. The estimator is able to reproduce the largest scales with reasonable accuracy for a range of wavenumber pairs, measurement locations and estimation locations. Importantly, the linear model is also able to predict with reasonable accuracy the performance that will be achieved by the estimator when applied to the DNS. A more practical estimation scheme using the shear stress at the wall as measurement is also considered. The estimator is still able to estimate the largest scales with reasonable accuracy, although the estimator’s performance is reduced.

Analysis of stability for stochastic delay integro-differential equations.

Science.gov (United States)

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

A speed estimation unit for induction motors based on adaptive linear combiner

International Nuclear Information System (INIS)

Marei, Mostafa I.; Shaaban, Mostafa F.; El-Sattar, Ahmed A.

2009-01-01

This paper presents a new induction motor speed estimation technique, which can estimate the rotor resistance as well, from the measured voltage and current signals. Moreover, the paper utilizes a novel adaptive linear combiner (ADALINE) structure for speed and rotor resistance estimations. This structure can deal with the multi-output systems and it is called MO-ADALINE. The model of the induction motor is arranged in a linear form, in the stationary reference frame, to cope with the proposed speed estimator. There are many advantages of the proposed unit such as wide speed range capability, immunity against harmonics of measured waveforms, and precise estimation of the speed and the rotor resistance at different dynamic changes. Different types of induction motor drive systems are used to evaluate the dynamic performance and to examine the accuracy of the proposed unit for speed and rotor resistance estimation.

Price Uncertainty in Linear Production Situations

NARCIS (Netherlands)

Suijs, J.P.M.

1999-01-01

This paper analyzes linear production situations with price uncertainty, and shows that the corrresponding stochastic linear production games are totally balanced. It also shows that investment funds, where investors pool their individual capital for joint investments in financial assets, fit into

Tightness of M-estimators for multiple linear regression in time series

DEFF Research Database (Denmark)

Johansen, Søren; Nielsen, Bent

We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness requires...

Modeling and identification of ARMG models for stochastic processes: application to on-line computation of the power spectral density

International Nuclear Information System (INIS)

Zwingelstein, Gilles; Thabet, Gabriel.

1977-01-01

Control algorithms for components of nuclear power plants are currently based on external diagnostic methods. Modeling and identification techniques for autoregressive moving average models (ARMA) for stochastic processes are described. The identified models provide a means of estimating the power spectral density with improved accuracy and computer time compared with the classical methods. They are particularly will suited for on-line estimation of the power spectral density. The observable stochastic process y (t) is modeled assuming that it is the output of a linear filter driven by Gaussian while noise w (t). Two identification schemes were tested to find the orders m and n of the ARMA (m,n) models and to estimate the parameters of the recursion equation relating the input and output signals. The first scheme consists in transforming the ARMA model to an autoregressive model. The parameters of this AR model are obtained using least squares estimation techniques. The second scheme consists in finding the parameters of the ARMA by nonlinear programming techniques. The power spectral density of y(t) is instantaneously deduced from these ARMA models [fr

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

Science.gov (United States)

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

Directory of Open Access Journals (Sweden)

Ling Zhang

2017-10-01

Full Text Available Abstract The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs. It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\\frac{1}{2}$ to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Robust synthetic biology design: stochastic game theory approach.

Science.gov (United States)

Chen, Bor-Sen; Chang, Chia-Hung; Lee, Hsiao-Ching

2009-07-15

Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi-Sugeno (T-S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf.

Inverse estimation of multiple muscle activations based on linear logistic regression.

Science.gov (United States)

Sekiya, Masashi; Tsuji, Toshiaki

2017-07-01

This study deals with a technology to estimate the muscle activity from the movement data using a statistical model. A linear regression (LR) model and artificial neural networks (ANN) have been known as statistical models for such use. Although ANN has a high estimation capability, it is often in the clinical application that the lack of data amount leads to performance deterioration. On the other hand, the LR model has a limitation in generalization performance. We therefore propose a muscle activity estimation method to improve the generalization performance through the use of linear logistic regression model. The proposed method was compared with the LR model and ANN in the verification experiment with 7 participants. As a result, the proposed method showed better generalization performance than the conventional methods in various tasks.

Estimating the effects of 17α-ethinylestradiol on stochastic population growth rate of fathead minnows: a population synthesis of empirically derived vital rates

Science.gov (United States)

Schwindt, Adam R.; Winkelman, Dana L.

2016-01-01

Urban freshwater streams in arid climates are wastewater effluent dominated ecosystems particularly impacted by bioactive chemicals including steroid estrogens that disrupt vertebrate reproduction. However, more understanding of the population and ecological consequences of exposure to wastewater effluent is needed. We used empirically derived vital rate estimates from a mesocosm study to develop a stochastic stage-structured population model and evaluated the effect of 17α-ethinylestradiol (EE2), the estrogen in human contraceptive pills, on fathead minnow Pimephales promelas stochastic population growth rate. Tested EE2 concentrations ranged from 3.2 to 10.9 ng L−1 and produced stochastic population growth rates (λ S ) below 1 at the lowest concentration, indicating potential for population decline. Declines in λ S compared to controls were evident in treatments that were lethal to adult males despite statistically insignificant effects on egg production and juvenile recruitment. In fact, results indicated that λ S was most sensitive to the survival of juveniles and female egg production. More broadly, our results document that population model results may differ even when empirically derived estimates of vital rates are similar among experimental treatments, and demonstrate how population models integrate and project the effects of stressors throughout the life cycle. Thus, stochastic population models can more effectively evaluate the ecological consequences of experimentally derived vital rates.

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D; Keesman, K.J.; Zwart, Heiko J.

In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D.; Keesman, K.J.; Zwart, H.

2006-01-01

Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state

Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

KAUST Repository

Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.

2014-01-01

This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

Pseudo-stochastic signal characterization in wavelet-domain

International Nuclear Information System (INIS)

Zaytsev, Kirill I; Zhirnov, Andrei A; Alekhnovich, Valentin I; Yurchenko, Stanislav O

2015-01-01

In this paper we present the method for fast and accurate characterization of pseudo-stochastic signals, which contain a large number of similar but randomly-located fragments. This method allows estimating the statistical characteristics of pseudo-stochastic signal, and it is based on digital signal processing in wavelet-domain. Continuous wavelet transform and the criterion for wavelet scale power density are utilized. We are experimentally implementing this method for the purpose of sand granulometry, and we are estimating the statistical parameters of test sand fractions

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

Pedjeu, Jean-C.; Ladde, Gangaram S.

2012-01-01

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

Science.gov (United States)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Project Evaluation and Cash Flow Forecasting by Stochastic Simulation

Directory of Open Access Journals (Sweden)

Odd A. Asbjørnsen

1983-10-01

Full Text Available The net present value of a discounted cash flow is used to evaluate projects. It is shown that the LaPlace transform of the cash flow time function is particularly useful when the cash flow profiles may be approximately described by ordinary linear differential equations in time. However, real cash flows are stochastic variables due to the stochastic nature of the disturbances during production.

Neutral Backward Stochastic Functional Differential Equations and Their Application

OpenAIRE

Wei, Wenning

2013-01-01

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an application, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.

Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

Directory of Open Access Journals (Sweden)

Mingzhu Song

2016-01-01

Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

A Bayes linear Bayes method for estimation of correlated event rates.

Science.gov (United States)

Quigley, John; Wilson, Kevin J; Walls, Lesley; Bedford, Tim

2013-12-01

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well-known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates. © 2013 Society for Risk Analysis.

Bounded Perturbation Regularization for Linear Least Squares Estimation

KAUST Repository

Ballal, Tarig

2017-10-18

This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

DETECTION OF CHANGES OF THE SYSTEM TECHNICAL STATE USING STOCHASTIC SUBSPACE OBSERVATION METHOD

Directory of Open Access Journals (Sweden)

Andrzej Puchalski

2014-03-01

Full Text Available System diagnostics based on vibroacoustics signals, carried out by means of stochastic subspace methods was undertaken in the hereby paper. Subspace methods are the ones based on numerical linear algebra tools. The considered solutions belong to diagnostic methods according to data, leading to the generation of residuals allowing failure recognition of elements and assemblies in machines and devices. The algorithm of diagnostics according to the subspace observation method was applied – in the paper – for the estimation of the valve system of the spark ignition engine.

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....

Linear kinetic theory and particle transport in stochastic mixtures. Third year and final report, June 15, 1993--December 14, 1996

International Nuclear Information System (INIS)

Pomraning, G.C.

1997-05-01

The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results

Reconstructing the hidden states in time course data of stochastic models.

Science.gov (United States)

Zimmer, Christoph

2015-11-01

Parameter estimation is central for analyzing models in Systems Biology. The relevance of stochastic modeling in the field is increasing. Therefore, the need for tailored parameter estimation techniques is increasing as well. Challenges for parameter estimation are partial observability, measurement noise, and the computational complexity arising from the dimension of the parameter space. This article extends the multiple shooting for stochastic systems' method, developed for inference in intrinsic stochastic systems. The treatment of extrinsic noise and the estimation of the unobserved states is improved, by taking into account the correlation between unobserved and observed species. This article demonstrates the power of the method on different scenarios of a Lotka-Volterra model, including cases in which the prey population dies out or explodes, and a Calcium oscillation system. Besides showing how the new extension improves the accuracy of the parameter estimates, this article analyzes the accuracy of the state estimates. In contrast to previous approaches, the new approach is well able to estimate states and parameters for all the scenarios. As it does not need stochastic simulations, it is of the same order of speed as conventional least squares parameter estimation methods with respect to computational time. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

Energy Technology Data Exchange (ETDEWEB)

Grain, Julien [Institut d' Astrophysique Spatiale, UMR8617, CNRS, Univ. Paris Sud, Université Paris-Saclay, Bt. 121, Orsay, F-91405 (France); Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO13FX (United Kingdom)

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Estimation of failure probabilities of linear dynamic systems by ...

Indian Academy of Sciences (India)

An iterative method for estimating the failure probability for certain time-variant reliability problems has been developed. In the paper, the focus is on the displacement response of a linear oscillator driven by white noise. Failure is then assumed to occur when the displacement response exceeds a critical threshold.

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...

Prospective national and regional environmental performance: Boundary estimations using a combined data envelopment - stochastic frontier analysis approach

International Nuclear Information System (INIS)

Vaninsky, Alexander

2010-01-01

The environmental performance of regions and largest economies of the world - actually, the efficiency of their energy sectors - is estimated for the period 2010-2030 by using forecasted values of main economic indicators. Two essentially different methodologies, data envelopment analysis and stochastic frontier analysis, are used to obtain upper and lower boundaries of the environmental efficiency index. Greenhouse gas emission per unit of area is used as a resulting indicator, with GDP, energy consumption, and population forming a background of comparable estimations. The dynamics of the upper and lower boundaries and their average is analyzed. Regions and national economies having low level or negative dynamics of environmental efficiency are determined.

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

NARCIS (Netherlands)

Jiang, G.J.; van der Sluis, P.J.

2000-01-01

This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the

Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem

Directory of Open Access Journals (Sweden)

V. Charles

2011-01-01

Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.

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...

Statistical inference and comparison of stochastic models for the hydraulic conductivity at the Finnsjoen-site

International Nuclear Information System (INIS)

Norman, S.

1992-04-01

The origin of this study was to find a good, or even the best, stochastic model for the hydraulic conductivity field at the Finnsjoe site. The conductivity field in question are regularized, that is upscaled. The reason for performing regularization of measurement data is primarily the need for long correlation scales. This is needed in order to model reasonably large domains that can be used when describing regional groundwater flow accurately. A theory of regularization is discussed in this report. In order to find the best model, jacknifing is employed to compare different stochastic models. The theory for this method is described. In the act of doing so we also take a look at linear predictor theory, so called kriging, and include a general discussion of stochastic functions and intrinsic random functions. The statistical inference methods for finding the models are also described, in particular regression, iterative generalized regression (IGLSE) and non-parametric variogram estimators. A large amount of results is presented for a regularization scale of 36 metre. (30 refs.) (au)

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

A Low-Complexity ESPRIT-Based DOA Estimation Method for Co-Prime Linear Arrays.

Science.gov (United States)

Sun, Fenggang; Gao, Bin; Chen, Lizhen; Lan, Peng

2016-08-25

The problem of direction-of-arrival (DOA) estimation is investigated for co-prime array, where the co-prime array consists of two uniform sparse linear subarrays with extended inter-element spacing. For each sparse subarray, true DOAs are mapped into several equivalent angles impinging on the traditional uniform linear array with half-wavelength spacing. Then, by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), the equivalent DOAs are estimated, and the candidate DOAs are recovered according to the relationship among equivalent and true DOAs. Finally, the true DOAs are estimated by combining the results of the two subarrays. The proposed method achieves a better complexity-performance tradeoff as compared to other existing methods.

Stochastic Modeling of Traffic Air Pollution

DEFF Research Database (Denmark)

Thoft-Christensen, Palle

2014-01-01

In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...

Using Spline Regression in Semi-Parametric Stochastic Frontier Analysis: An Application to Polish Dairy Farms

DEFF Research Database (Denmark)

Czekaj, Tomasz Gerard; Henningsen, Arne

of specifying an unsuitable functional form and thus, model misspecification and biased parameter estimates. Given these problems of the DEA and the SFA, Fan, Li and Weersink (1996) proposed a semi-parametric stochastic frontier model that estimates the production function (frontier) by non......), Kumbhakar et al. (2007), and Henningsen and Kumbhakar (2009). The aim of this paper and its main contribution to the existing literature is the estimation semi-parametric stochastic frontier models using a different non-parametric estimation technique: spline regression (Ma et al. 2011). We apply...... efficiency of Polish dairy farms contributes to the insight into this dynamic process. Furthermore, we compare and evaluate the results of this spline-based semi-parametric stochastic frontier model with results of other semi-parametric stochastic frontier models and of traditional parametric stochastic...

Redshift space correlations and scale-dependent stochastic biasing of density peaks

Science.gov (United States)

Desjacques, Vincent; Sheth, Ravi K.

2010-01-01

We calculate the redshift space correlation function and the power spectrum of density peaks of a Gaussian random field. Our derivation, which is valid on linear scales k≲0.1hMpc-1, is based on the peak biasing relation given by Desjacques [Phys. Rev. DPRVDAQ1550-7998, 78, 103503 (2008)10.1103/PhysRevD.78.103503]. In linear theory, the redshift space power spectrum is Ppks(k,μ)=exp⁡(-f2σvel2k2μ2)[bpk(k)+bvel(k)fμ2]2Pδ(k), where μ is the angle with respect to the line of sight, σvel is the one-dimensional velocity dispersion, f is the growth rate, and bpk(k) and bvel(k) are k-dependent linear spatial and velocity bias factors. For peaks, the value of σvel depends upon the functional form of bvel. When the k dependence is absent from the square brackets and bvel is set to unity, the resulting expression is assumed to describe models where the bias is linear and deterministic, but the velocities are unbiased. The peak model is remarkable because it has unbiased velocities in this same sense—peak motions are driven by dark matter flows—but, in order to achieve this, bvel must be k dependent. We speculate that this is true in general: k dependence of the spatial bias will lead to k dependence of bvel even if the biased tracers flow with the dark matter. Because of the k dependence of the linear bias parameters, standard manipulations applied to the peak model will lead to k-dependent estimates of the growth factor that could erroneously be interpreted as a signature of modified dark energy or gravity. We use the Fisher formalism to show that the constraint on the growth rate f is degraded by a factor of 2 if one allows for a k-dependent velocity bias of the peak type. Our analysis also demonstrates that the Gaussian smoothing term is part and parcel of linear theory. We discuss a simple estimate of nonlinear evolution and illustrate the effect of the peak bias on the redshift space multipoles. For k≲0.1hMpc-1, the peak bias is deterministic but k

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.

Chance-constrained/stochastic linear programming model for acid rain abatement. I. Complete colinearity and noncolinearity

Energy Technology Data Exchange (ETDEWEB)

Ellis, J H; McBean, E A; Farquhar, G J

1985-01-01

A Linear Programming model is presented for development of acid rain abatement strategies in eastern North America. For a system comprised of 235 large controllable point sources and 83 uncontrolled area sources, it determines the least-cost method of reducing SO/sub 2/ emissions to satisfy maximum wet sulfur deposition limits at 20 sensitive receptor locations. In this paper, the purely deterministic model is extended to a probabilistic form by incorporating the effects of meteorologic variability on the long-range pollutant transport processes. These processes are represented by source-receptor-specific transfer coefficients. Experiments for quantifying the spatial variability of transfer coefficients showed their distributions to be approximately lognormal with logarithmic standard deviations consistently about unity. Three methods of incorporating second-moment random variable uncertainty into the deterministic LP framework are described: Two-Stage Programming Under Uncertainty, Chance-Constrained Programming and Stochastic Linear Programming. A composite CCP-SLP model is developed which embodies the two-dimensional characteristics of transfer coefficient uncertainty. Two probabilistic formulations are described involving complete colinearity and complete noncolinearity for the transfer coefficient covariance-correlation structure. The completely colinear and noncolinear formulations are considered extreme bounds in a meteorologic sense and yield abatement strategies of largely didactic value. Such strategies can be characterized as having excessive costs and undesirable deposition results in the completely colinear case and absence of a clearly defined system risk level (other than expected-value) in the noncolinear formulation.

truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models

Directory of Open Access Journals (Sweden)

Maria Karlsson

2014-05-01

Full Text Available Problems with truncated data occur in many areas, complicating estimation and inference. Regarding linear regression models, the ordinary least squares estimator is inconsistent and biased for these types of data and is therefore unsuitable for use. Alternative estimators, designed for the estimation of truncated regression models, have been developed. This paper presents the R package truncSP. The package contains functions for the estimation of semi-parametric truncated linear regression models using three different estimators: the symmetrically trimmed least squares, quadratic mode, and left truncated estimators, all of which have been shown to have good asymptotic and ?nite sample properties. The package also provides functions for the analysis of the estimated models. Data from the environmental sciences are used to illustrate the functions in the package.

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.

Stochastic growth of localized plasma waves

International Nuclear Information System (INIS)

Robinson, P.A.; Cairns, Iver H.

2001-01-01

Localized bursty plasma waves are detected by spacecraft in many space plasmas. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the system, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it far longer than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. These mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing and power-law distributed in strong turbulence. Recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type III solar radio sources, the Earth's foreshock, magnetosheath, and polar cap regions. It is shown that when combined with wave-wave processes, SGT also accounts for associated radio emissions

Stability analysis for stochastic BAM nonlinear neural network with delays

Science.gov (United States)

Lv, Z. W.; Shu, H. S.; Wei, G. L.

2008-02-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.

Stability analysis for stochastic BAM nonlinear neural network with delays

International Nuclear Information System (INIS)

Lv, Z W; Shu, H S; Wei, G L

2008-01-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria

Explicit estimating equations for semiparametric generalized linear latent variable models

KAUST Repository

Ma, Yanyuan

2010-07-05

We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.

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.

Forecasting financial asset processes: stochastic dynamics via learning neural networks.

Science.gov (United States)

Giebel, S; Rainer, M

2010-01-01

Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

Robust best linear estimation for regression analysis using surrogate and instrumental variables.

Science.gov (United States)

Wang, C Y

2012-04-01

We investigate methods for regression analysis when covariates are measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies the classical measurement error model, but it may not have repeated measurements. In addition to the surrogate variables that are available among the subjects in the calibration sample, we assume that there is an instrumental variable (IV) that is available for all study subjects. An IV is correlated with the unobserved true exposure variable and hence can be useful in the estimation of the regression coefficients. We propose a robust best linear estimator that uses all the available data, which is the most efficient among a class of consistent estimators. The proposed estimator is shown to be consistent and asymptotically normal under very weak distributional assumptions. For Poisson or linear regression, the proposed estimator is consistent even if the measurement error from the surrogate or IV is heteroscedastic. Finite-sample performance of the proposed estimator is examined and compared with other estimators via intensive simulation studies. The proposed method and other methods are applied to a bladder cancer case-control study.

A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

Energy Technology Data Exchange (ETDEWEB)

Melboe, Hallgeir

2001-10-01

This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

International Nuclear Information System (INIS)

Rupšys, P.

2015-01-01

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE

Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

Science.gov (United States)

Krylov, N. V.; Priola, E.

2017-09-01

We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

Energy Technology Data Exchange (ETDEWEB)

Rupšys, P. [Aleksandras Stulginskis University, Studenų g. 11, Akademija, Kaunas district, LT – 53361 Lithuania (Lithuania)

2015-10-28

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

Existence and density theorems for stochastic maps on commutative C*-algebras

International Nuclear Information System (INIS)

Alberti, P.M.; Uhlmann, A.

1979-06-01

Theorems are presented on the structure of stochastic and normalized positive linear maps over commutative C*-algebras. It is shown how strongly the solution of the n-tupel problem for stochastic maps relates to the fact that stochastic maps of finite rank are weakly dense within stochastic maps in case of a commutative C*-algebra. A new proof of the density theorem is given and (besides the solution of the n-tupel problem) results are derived concerning the extremal maps of certain convex subsets which are weakly dense. All stated facts suggest application in statistical physics (algebraic approach), especially concerning questions around evolution of classical systems. (author)

From neurons to circuits: linear estimation of local field potentials

Science.gov (United States)

Rasch, Malte; Logthetis, Nikos K.; Kreiman, Gabriel

2010-01-01

Extracellular physiological recordings are typically separated into two frequency bands: local field potentials (LFPs, a circuit property) and spiking multi-unit activity (MUA). There has been increased interest in LFPs due to their correlation with fMRI measurements and the possibility of studying local processing and neuronal synchrony. To further understand the biophysical origin of LFPs, we asked whether it is possible to estimate their time course based on the spiking activity from the same or nearby electrodes. We used Signal Estimation Theory to show that a linear filter operation on the activity of one/few neurons can explain a significant fraction of the LFP time course in the macaque primary visual cortex. The linear filter used to estimate the LFPs had a stereotypical shape characterized by a sharp downstroke at negative time lags and a slower positive upstroke for positve time lags. The filter was similar across neocortical regions and behavioral conditions including spontaneous activity and visual stimulation. The estimations had a spatial resolution of ~1 mm and a temporal resolution of ~200 ms. By considering a causal filter, we observed a temporal asymmetry such that the positive time lags in the filter contributed more to the LFP estimation than negative time lags. Additionally, we showed that spikes occurring within ~10 ms of spikes from nearby neurons yielded better estimation accuracies than nonsynchronous spikes. In sum, our results suggest that at least some circuit-level local properties of the field potentials can be predicted from the activity of one or a few neurons. PMID:19889990

Fitting Social Network Models Using Varying Truncation Stochastic Approximation MCMC Algorithm

KAUST Repository

Jin, Ick Hoon

2013-10-01

The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Simultaneous Event-Triggered Fault Detection and Estimation for Stochastic Systems Subject to Deception Attacks.

Science.gov (United States)

Li, Yunji; Wu, QingE; Peng, Li

2018-01-23

In this paper, a synthesized design of fault-detection filter and fault estimator is considered for a class of discrete-time stochastic systems in the framework of event-triggered transmission scheme subject to unknown disturbances and deception attacks. A random variable obeying the Bernoulli distribution is employed to characterize the phenomena of the randomly occurring deception attacks. To achieve a fault-detection residual is only sensitive to faults while robust to disturbances, a coordinate transformation approach is exploited. This approach can transform the considered system into two subsystems and the unknown disturbances are removed from one of the subsystems. The gain of fault-detection filter is derived by minimizing an upper bound of filter error covariance. Meanwhile, system faults can be reconstructed by the remote fault estimator. An recursive approach is developed to obtain fault estimator gains as well as guarantee the fault estimator performance. Furthermore, the corresponding event-triggered sensor data transmission scheme is also presented for improving working-life of the wireless sensor node when measurement information are aperiodically transmitted. Finally, a scaled version of an industrial system consisting of local PC, remote estimator and wireless sensor node is used to experimentally evaluate the proposed theoretical results. In particular, a novel fault-alarming strategy is proposed so that the real-time capacity of fault-detection is guaranteed when the event condition is triggered.

Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

Directory of Open Access Journals (Sweden)

Feten Gannouni

2017-01-01

Full Text Available We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.

Stochastic Dominance under the Nonlinear Expected Utilities

Directory of Open Access Journals (Sweden)

Xinling Xiao

2014-01-01

Full Text Available In 1947, von Neumann and Morgenstern introduced the well-known expected utility and the related axiomatic system (see von Neumann and Morgenstern (1953. It is widely used in economics, for example, financial economics. But the well-known Allais paradox (see Allais (1979 shows that the linear expected utility has some limitations sometimes. Because of this, Peng proposed a concept of nonlinear expected utility (see Peng (2005. In this paper we propose a concept of stochastic dominance under the nonlinear expected utilities. We give sufficient conditions on which a random choice X stochastically dominates a random choice Y under the nonlinear expected utilities. We also provide sufficient conditions on which a random choice X strictly stochastically dominates a random choice Y under the sublinear expected utilities.

Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition

KAUST Repository

Bessaih, Hakima

2015-11-02

The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.

Estimation of the limit of detection in semiconductor gas sensors through linearized calibration models.

Science.gov (United States)

Burgués, Javier; Jiménez-Soto, Juan Manuel; Marco, Santiago

2018-07-12

The limit of detection (LOD) is a key figure of merit in chemical sensing. However, the estimation of this figure of merit is hindered by the non-linear calibration curve characteristic of semiconductor gas sensor technologies such as, metal oxide (MOX), gasFETs or thermoelectric sensors. Additionally, chemical sensors suffer from cross-sensitivities and temporal stability problems. The application of the International Union of Pure and Applied Chemistry (IUPAC) recommendations for univariate LOD estimation in non-linear semiconductor gas sensors is not straightforward due to the strong statistical requirements of the IUPAC methodology (linearity, homoscedasticity, normality). Here, we propose a methodological approach to LOD estimation through linearized calibration models. As an example, the methodology is applied to the detection of low concentrations of carbon monoxide using MOX gas sensors in a scenario where the main source of error is the presence of uncontrolled levels of humidity. Copyright © 2018 Elsevier B.V. All rights reserved.

Stochastic Estimation Methods for Induction Motor Transient Thermal Monitoring Under Non Linear Condition

Directory of Open Access Journals (Sweden)

Mellah HACEN

2012-08-01

Full Text Available The induction machine, because of its robustness and low-cost, is commonly used in the industry. Nevertheless, as every type of electrical machine, this machine suffers of some limitations. The most important one is the working temperature which is the dimensioning parameter for the definition of the nominal working point and the machine lifetime. Due to a strong demand concerning thermal monitoring methods appeared in the industry sector. In this context, the adding of temperature sensors is not acceptable and the studied methods tend to use sensorless approaches such as observators or parameters estimators like the extended Kalman Filter (EKF. Then the important criteria are reliability, computational cost ad real time implementation.

Convergence of trajectories in fractal interpolation of stochastic processes

International Nuclear Information System (INIS)

MaIysz, Robert

2006-01-01

The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation

Preconditioned stochastic gradient descent optimisation for monomodal image registration

NARCIS (Netherlands)

Klein, S.; Staring, M.; Andersson, J.P.; Pluim, J.P.W.; Fichtinger, G.; Martel, A.; Peters, T.

2011-01-01

We present a stochastic optimisation method for intensity-based monomodal image registration. The method is based on a Robbins-Monro stochastic gradient descent method with adaptive step size estimation, and adds a preconditioning matrix. The derivation of the pre-conditioner is based on the

On the small-time behavior of stochastic logistic models

Directory of Open Access Journals (Sweden)

Dung Tien Nguyen

2017-09-01

Full Text Available In this paper we investigate the small-time behaviors of the solution to  a stochastic logistic model. The obtained results allow us to estimate the number of individuals in the population and can be used to study stochastic prey-predator systems.

Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data

KAUST Repository

Cheng, Guang; Zhou, Lan; Huang, Jianhua Z.

2014-01-01

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based

Bounds and estimates for the linearly perturbed eigenvalue problem

International Nuclear Information System (INIS)

Raddatz, W.D.

1983-01-01

This thesis considers the problem of bounding and estimating the discrete portion of the spectrum of a linearly perturbed self-adjoint operator, M(x). It is supposed that one knows an incomplete set of data consisting in the first few coefficients of the Taylor series expansions of one or more of the eigenvalues of M(x) about x = 0. The foundations of the variational study of eigen-values are first presented. These are then used to construct the best possible upper bounds and estimates using various sets of given information. Lower bounds are obtained by estimating the error in the upper bounds. The extension of these bounds and estimates to the eigenvalues of the doubly-perturbed operator M(x,y) is discussed. The results presented have numerous practical application in the physical sciences, including problems in atomic physics and the theory of vibrations of acoustical and mechanical systems

The response of a linear monostable system and its application in parameters estimation for PSK signals

International Nuclear Information System (INIS)

Duan, Chaowei; Zhan, Yafeng

2016-01-01

The output characteristics of a linear monostable system driven with a periodic signal and an additive white Gaussian noise are studied in this paper. Theoretical analysis shows that the output signal-to-noise ratio (SNR) decreases monotonously with the increasing noise intensity but the output SNR-gain is stable. Inspired by this high SNR-gain phenomenon, this paper applies the linear monostable system in the parameters estimation algorithm for phase shift keying (PSK) signals and improves the estimation performance. - Highlights: • The response of a linear monostable system driven with a periodic signal and an additive white Gaussian noise is analyzed. • The optimal parameter of this linear monostable system to maximum the output SNR-gain is obtained. • Application of this linear monostable system in parameters estimation algorithm for PSK signals obtains performance improvement.

Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

KAUST Repository

Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

2017-01-01

This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating

The stochastic seasonal behavior of energy commodity convenience yields

International Nuclear Information System (INIS)

Mirantes, Andrés García; Población, Javier; Serna, Gregorio

2013-01-01

This paper contributes to the commodity pricing literature by consistently modeling the convenience yield with its empirically observed properties. Specifically, in this paper, we show how a four-factor model for the stochastic behavior of commodity prices, with two long- and short-term factors and two additional seasonal factors, may accommodate some of the most important empirically observed characteristics of commodity convenience yields, such as the mean reversion and stochastic seasonality. Based on this evidence, a theoretical model is presented and estimated to characterize the commodity convenience yield dynamics that are consistent with previous findings. We also show that commodity price seasonality is better estimated through convenience yields than through futures prices. - Highlights: • Energy commodity convenience yields exhibit mean reversion and stochastic seasonality. • We present a model for convenience yields accounting for their observed characteristics. • Commodity price seasonality is better estimated through convenience yields

Stochastic motion of particles in tandem mirror devices

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Kamimura, T.

1982-01-01

Stochastic motion of particles in tandem mirror devices is examined on basis of a nonlinear mapping of particle positions on the equatorial plane. Local stability analysis provides detailed informations on particle trajectories. The rate of stochastic plasma diffusion is estimated from numerical observations of motions of particles over a large number of time steps. (author)

Pose and Motion Estimation Using Dual Quaternion-Based Extended Kalman Filtering

Energy Technology Data Exchange (ETDEWEB)

Goddard, J.S.; Abidi, M.A.

1998-06-01

A solution to the remote three-dimensional (3-D) measurement problem is presented for a dynamic system given a sequence of two-dimensional (2-D) intensity images of a moving object. The 3-D transformation is modeled as a nonlinear stochastic system with the state estimate providing the six-degree-of-freedom motion and position values as well as structure. The stochastic model uses the iterated extended Kalman filter (IEKF) as a nonlinear estimator and a screw representation of the 3-D transformation based on dual quaternions. Dual quaternions, whose elements are dual numbers, provide a means to represent both rotation and translation in a unified notation. Linear object features, represented as dual vectors, are transformed using the dual quaternion transformation and are then projected to linear features in the image plane. The method has been implemented and tested with both simulated and actual experimental data. Simulation results are provided, along with comparisons to a point-based IEKF method using rotation and translation, to show the relative advantages of this method. Experimental results from testing using a camera mounted on the end effector of a robot arm are also given.

Compressible cavitation with stochastic field method

Science.gov (United States)

Class, Andreas; Dumond, Julien

2012-11-01

Non-linear 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 Lagrange 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 Euler fields has been proposed which eliminates the necessity to mix Euler and Lagrange techniques or prescribed pdf assumptions. In the present work, part of the PhD Design and analysis of a Passive Outflow Reducer relying on cavitation, a first application of the stochastic field method to multi-phase flow and in particular to cavitating flow is presented. The application considered is a nozzle subjected to high velocity flow so that sheet cavitation is observed near the nozzle surface in the divergent section. It is demonstrated that the stochastic field formulation captures the wide range of pdf shapes present at different locations. The method is compatible with finite-volume codes where all existing physical models available for Lagrange techniques, presumed pdf or binning methods can be easily extended to the stochastic field formulation.

Doubly stochastic radial basis function methods

Science.gov (United States)

Yang, Fenglian; Yan, Liang; Ling, Leevan

2018-06-01

We propose a doubly stochastic radial basis function (DSRBF) method for function recoveries. Instead of a constant, we treat the RBF shape parameters as stochastic variables whose distribution were determined by a stochastic leave-one-out cross validation (LOOCV) estimation. A careful operation count is provided in order to determine the ranges of all the parameters in our methods. The overhead cost for setting up the proposed DSRBF method is O (n2) for function recovery problems with n basis. Numerical experiments confirm that the proposed method not only outperforms constant shape parameter formulation (in terms of accuracy with comparable computational cost) but also the optimal LOOCV formulation (in terms of both accuracy and computational cost).

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

Beta Instability and Stochastic Market Weights

OpenAIRE

David H. Goldenberg

1985-01-01

An argument is given for individual firm beta instability based upon the stochastic character of the market weights defining the market portfolio and the constancy of its beta. This argument is generalized to market weighted portfolios and the form of the stochastic process generating betas is linked to that of the market return process. The implications of this analysis for adequacy of models of beta nonstationarity and estimation of betas are considered in light of the available empirical e...

Stochastic light-cone CTMRG: a new DMRG approach to stochastic models 02.50.Ey Stochastic processes; 64.60.Ht Dynamic critical phenomena; 02.70.-c Computational techniques; 05.10.Cc Renormalization group methods;

CERN Document Server

Kemper, A; Nishino, T; Schadschneider, A; Zittartz, J

2003-01-01

We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10 sup 5 shows a considerable improvement on the old stochastic TMRG algorithm.

Short-term memories with a stochastic perturbation

International Nuclear Information System (INIS)

Pontes, Jose C.A. de; Batista, Antonio M.; Viana, Ricardo L.; Lopes, Sergio R.

2005-01-01

We investigate short-term memories in linear and weakly nonlinear coupled map lattices with a periodic external input. We use locally coupled maps to present numerical results about short-term memory formation adding a stochastic perturbation in the maps and in the external input

Estimating and interpreting a common stochastic component for the Brazilian industrial production index

Directory of Open Access Journals (Sweden)

Paulo Picchetti

2002-03-01

Full Text Available This paper employs a state-space formulation to model a common stochastic component in four different series that constitute the aggregate index of industrial production in Brazil. This estimated common component is then interpreted as a measurement of behavior of fundamentals in the brazilian economy and compared to the actual aggregate index.A partir de uma formulação em espaço de estado, modelamos um componente estocástico comum para quatro séries distintas que compõem o índice agregado de produção industrial calculado pelo IBGE para o Brasil. Esse componente estocástico comum estimado é então interpretado como uma medida do comportamento de fundamentos da economia brasileira, e comparado com o índice agregado efetivo.

Stochastic Frontier Estimation of Efficient Learning in Video Games

Science.gov (United States)

Hamlen, Karla R.

2012-01-01

Stochastic Frontier Regression Analysis was used to investigate strategies and skills that are associated with the minimization of time required to achieve proficiency in video games among students in grades four and five. Students self-reported their video game play habits, including strategies and skills used to become good at the video games…

Event-Triggered Faults Tolerant Control for Stochastic Systems with Time Delays

Directory of Open Access Journals (Sweden)

Ling Huang

2016-01-01

Full Text Available This paper is concerned with the state-feedback controller design for stochastic networked control systems (NCSs with random actuator failures and transmission delays. Firstly, an event-triggered scheme is introduced to optimize the performance of the stochastic NCSs. Secondly, stochastic NCSs under event-triggered scheme are modeled as stochastic time-delay systems. Thirdly, some less conservative delay-dependent stability criteria in terms of linear matrix inequalities for the codesign of both the controller gain and the trigger parameters are obtained by using delay-decomposition technique and convex combination approach. Finally, a numerical example is provided to show the less sampled data transmission and less conservatism of the proposed theory.