Stochastic Optimal Control in Infinite Dimension

Stochastic Optimal Control in Infinite Dimension
Title Stochastic Optimal Control in Infinite Dimension PDF eBook
Author Giorgio Fabbri
Publisher Springer
Pages 928
Release 2017-06-22
Genre Mathematics
ISBN 3319530674

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Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Optimal Control Theory for Infinite Dimensional Systems

Optimal Control Theory for Infinite Dimensional Systems
Title Optimal Control Theory for Infinite Dimensional Systems PDF eBook
Author Xungjing Li
Publisher Springer Science & Business Media
Pages 462
Release 2012-12-06
Genre Mathematics
ISBN 1461242606

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Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.

Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential Equations with Applications
Title Stability of Infinite Dimensional Stochastic Differential Equations with Applications PDF eBook
Author Kai Liu
Publisher CRC Press
Pages 311
Release 2005-08-23
Genre Mathematics
ISBN 1420034820

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Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ

Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics

Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics
Title Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics PDF eBook
Author Wilfried Grecksch
Publisher World Scientific
Pages 261
Release 2020-04-22
Genre Science
ISBN 9811209804

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This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.

An Introduction to Infinite-Dimensional Analysis

An Introduction to Infinite-Dimensional Analysis
Title An Introduction to Infinite-Dimensional Analysis PDF eBook
Author Giuseppe Da Prato
Publisher Springer Science & Business Media
Pages 217
Release 2006-08-25
Genre Mathematics
ISBN 3540290214

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Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.

Ergodicity for Infinite Dimensional Systems

Ergodicity for Infinite Dimensional Systems
Title Ergodicity for Infinite Dimensional Systems PDF eBook
Author Giuseppe Da Prato
Publisher Cambridge University Press
Pages 355
Release 1996-05-16
Genre Mathematics
ISBN 0521579007

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This is the only book on stochastic modelling of infinite dimensional dynamical systems.

Deterministic and Stochastic Optimal Control and Inverse Problems

Deterministic and Stochastic Optimal Control and Inverse Problems
Title Deterministic and Stochastic Optimal Control and Inverse Problems PDF eBook
Author Baasansuren Jadamba
Publisher CRC Press
Pages 394
Release 2021-12-15
Genre Computers
ISBN 1000511723

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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.