Estimation And Control Problems For Stochastic Partial Differential Equations

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Estimation and Control Problems for Stochastic Partial Differential Equations

Author : Pavel S. Knopov
Publisher : Springer Science & Business Media
ISBN 13 : 1461482860
Total Pages : 191 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Estimation and Control Problems for Stochastic Partial Differential Equations by : Pavel S. Knopov

Download or read book Estimation and Control Problems for Stochastic Partial Differential Equations written by Pavel S. Knopov and published by Springer Science & Business Media. This book was released on 2013-09-17 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered. More generally, this book is intended for scientists, graduate, and post-graduates specializing in probability theory and mathematical statistics. The models presented describe many processes in turbulence theory, fluid mechanics, hydrology, astronomy, and meteorology, and are widely used in pattern recognition theory and parameter identification of stochastic systems. Therefore, this book may also be useful to applied mathematicians who use probability and statistical methods in the selection of useful signals subject to noise, hypothesis distinguishing, distributed parameter systems optimal control, and more. Material presented in this monograph can be used for education courses on the estimation and control theory of random fields.

Mathematical Control Theory for Stochastic Partial Differential Equations

Author : Qi Lü
Publisher : Springer Nature
ISBN 13 : 3030823318
Total Pages : 592 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Mathematical Control Theory for Stochastic Partial Differential Equations by : Qi Lü

Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü and published by Springer Nature. This book was released on 2021-10-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Deterministic and Stochastic Optimal Control and Inverse Problems

Author : Baasansuren Jadamba
Publisher : CRC Press
ISBN 13 : 1000511723
Total Pages : 394 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Deterministic and Stochastic Optimal Control and Inverse Problems by : Baasansuren Jadamba

Download or read book Deterministic and Stochastic Optimal Control and Inverse Problems written by Baasansuren Jadamba and published by CRC Press. This book was released on 2021-12-15 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.

Recursive Estimation and Control for Stochastic Systems

Author : Hanfu Chen
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Recursive Estimation and Control for Stochastic Systems by : Hanfu Chen

Download or read book Recursive Estimation and Control for Stochastic Systems written by Hanfu Chen and published by John Wiley & Sons. This book was released on 1985 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained reference for statisticians and engineers in system and control theory, analyzes the effect of convergent recursive estimation algorithms and stochastic approximation on the dependent noise case and the classic independent case. It discusses control and adaptive control problems related to recursive estimation, and introduces the combined probabilistic and differential equation method of data analysis.

Parameter Estimation in Stochastic Differential Equations

Author : Jaya P. N. Bishwal
Publisher : Springer
ISBN 13 : 3540744487
Total Pages : 271 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Parameter Estimation in Stochastic Differential Equations by : Jaya P. N. Bishwal

Download or read book Parameter Estimation in Stochastic Differential Equations written by Jaya P. N. Bishwal and published by Springer. This book was released on 2007-09-26 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. 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.

Stochastic Processes, Estimation, and Control

Author : Jason L. Speyer
Publisher : SIAM
ISBN 13 : 0898718597
Total Pages : 392 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Stochastic Processes, Estimation, and Control by : Jason L. Speyer

Download or read book Stochastic Processes, Estimation, and Control written by Jason L. Speyer and published by SIAM. This book was released on 2008-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.

Stochastic Differential Systems, Stochastic Control Theory and Applications

Author : Wendell Fleming
Publisher : Springer Science & Business Media
ISBN 13 : 1461387620
Total Pages : 601 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Stochastic Differential Systems, Stochastic Control Theory and Applications by : Wendell Fleming

Download or read book Stochastic Differential Systems, Stochastic Control Theory and Applications written by Wendell Fleming and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications STOCHASTIC DIFFERENTIAL SYSTEMS, STOCHASTIC CONTROL THEORY AND APPLICATIONS is the proceedings of a workshop which was an integral part of the 1986-87 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS. We are grateful to the Scientific Committee: Daniel Stroock (Chairman) WendeIl Flerning Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We es pecially thank WendeIl Fleming and Pierre-Louis Lions for organizing an interesting and productive workshop in an area in which mathematics is beginning to make significant contributions to real-world problems. George R. Seil Hans Weinberger PREFACE This volume is the Proceedings of a Workshop on Stochastic Differential Systems, Stochastic Control Theory, and Applications held at IMA June 9-19,1986. The Workshop Program Commit tee consisted of W.H. Fleming and P.-L. Lions (co-chairmen), J. Baras, B. Hajek, J.M. Harrison, and H. Sussmann. The Workshop emphasized topics in the following four areas. (1) Mathematical theory of stochastic differential systems, stochastic control and nonlinear filtering for Markov diffusion processes. Connections with partial differential equations. (2) Applications of stochastic differential system theory, in engineering and management sci ence. Adaptive control of Markov processes. Advanced computational methods in stochas tic control and nonlinear filtering. (3) Stochastic scheduling, queueing networks, and related topics. Flow control, multiarm bandit problems, applications to problems of computer networks and scheduling of complex manufacturing operations.

Stochastic Differential and Difference Equations

Author : Imre Csiszar
Publisher : Springer Science & Business Media
ISBN 13 : 1461219809
Total Pages : 358 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Differential and Difference Equations by : Imre Csiszar

Download or read book Stochastic Differential and Difference Equations written by Imre Csiszar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Control Theory of Systems Governed by Partial Differential Equations

Author : A.K. Aziz
Publisher : Academic Press
ISBN 13 : 1483216306
Total Pages : 289 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Control Theory of Systems Governed by Partial Differential Equations by : A.K. Aziz

Download or read book Control Theory of Systems Governed by Partial Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.

Model Reduction of Parametrized Systems

Author : Peter Benner
Publisher : Springer
ISBN 13 : 3319587862
Total Pages : 503 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Model Reduction of Parametrized Systems by : Peter Benner

Download or read book Model Reduction of Parametrized Systems written by Peter Benner and published by Springer. This book was released on 2017-09-05 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Carleman Estimates for Second Order Partial Differential Operators and Applications

Author : Xiaoyu Fu
Publisher : Springer Nature
ISBN 13 : 3030295303
Total Pages : 127 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Carleman Estimates for Second Order Partial Differential Operators and Applications by : Xiaoyu Fu

Download or read book Carleman Estimates for Second Order Partial Differential Operators and Applications written by Xiaoyu Fu and published by Springer Nature. This book was released on 2019-10-31 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.

Stochastic Partial Differential Equations, Second Edition

Author : Pao-Liu Chow
Publisher : CRC Press
ISBN 13 : 1466579552
Total Pages : 336 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Stochastic Partial Differential Equations, Second Edition by : Pao-Liu Chow

Download or read book Stochastic Partial Differential Equations, Second Edition written by Pao-Liu Chow and published by CRC Press. This book was released on 2014-12-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.

Applied Stochastic Differential Equations

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä

Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Numerical Methods and Deep Learning for Stochastic Control Problems and Partial Differential Equations

Author : Come Huré
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (118 download)

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Book Synopsis Numerical Methods and Deep Learning for Stochastic Control Problems and Partial Differential Equations by : Come Huré

Download or read book Numerical Methods and Deep Learning for Stochastic Control Problems and Partial Differential Equations written by Come Huré and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present thesis deals with numerical schemes to solve Markov Decision Problems (MDPs), partial differential equations (PDEs), quasi-variational inequalities (QVIs), backward stochastic differential equations (BSDEs) and reflected backward stochastic differential equations (RBSDEs). The thesis is divided into three parts.The first part focuses on methods based on quantization, local regression and global regression to solve MDPs. Firstly, we present a new algorithm, named Qknn, and study its consistency. A time-continuous control problem of market-making is then presented, which is theoretically solved by reducing the problem to a MDP, and whose optimal control is accurately approximated by Qknn. Then, a method based on Markovian embedding is presented to reduce McKean-Vlasov control prob- lem with partial information to standard MDP. This method is applied to three different McKean- Vlasov control problems with partial information. The method and high accuracy of Qknn is validated by comparing the performance of the latter with some finite difference-based algorithms and some global regression-based algorithm such as regress-now and regress-later.In the second part of the thesis, we propose new algorithms to solve MDPs in high-dimension. Neural networks, combined with gradient-descent methods, have been empirically proved to be the best at learning complex functions in high-dimension, thus, leading us to base our new algorithms on them. We derived the theoretical rates of convergence of the proposed new algorithms, and tested them on several relevant applications.In the third part of the thesis, we propose a numerical scheme for PDEs, QVIs, BSDEs, and RBSDEs. We analyze the performance of our new algorithms, and compare them to other ones available in the literature (including the recent one proposed in [EHJ17]) on several tests, which illustrates the efficiency of our methods to estimate complex solutions in high-dimension.Keywords: Deep learning, neural networks, Stochastic control, Markov Decision Process, non- linear PDEs, QVIs, optimal stopping problem BSDEs, RBSDEs, McKean-Vlasov control, perfor- mance iteration, value iteration, hybrid iteration, global regression, local regression, regress-later, quantization, limit order book, pure-jump controlled process, algorithmic-trading, market-making, high-dimension.

Probabilistic Analysis and Related Topics

Author : A. T. Bharucha-Reid
Publisher : Elsevier
ISBN 13 : 1483276651
Total Pages : 250 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Probabilistic Analysis and Related Topics by : A. T. Bharucha-Reid

Download or read book Probabilistic Analysis and Related Topics written by A. T. Bharucha-Reid and published by Elsevier. This book was released on 2014-05-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.

Stochastic Partial Differential Equations

Author : Pao-Liu Chow
Publisher : CRC Press
ISBN 13 : 1000738213
Total Pages : 296 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Stochastic Partial Differential Equations by : Pao-Liu Chow

Download or read book Stochastic Partial Differential Equations written by Pao-Liu Chow and published by CRC Press. This book was released on 2007-03-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theor

Trends in Control Theory and Partial Differential Equations

Author : Fatiha Alabau-Boussouira
Publisher : Springer
ISBN 13 : 3030179494
Total Pages : 276 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Trends in Control Theory and Partial Differential Equations by : Fatiha Alabau-Boussouira

Download or read book Trends in Control Theory and Partial Differential Equations written by Fatiha Alabau-Boussouira and published by Springer. This book was released on 2019-07-04 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.