Controlled Diffusion Processes

Author : N. V. Krylov
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 50,5 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783540709145

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Controlled Diffusion Processes by N. V. Krylov Pdf

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

Author : N.V. Krylov
Publisher : Springer
Page : 0 pages
File Size : 40,7 Mb
Release : 1980-11-12
Category : Mathematics
ISBN : 0387904611

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Controlled Diffusion Processes by N.V. Krylov Pdf

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. During that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in W onham [76J). At the same time, Girsanov [25J and Howard [26J made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4J. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8J, Mine and Osaki [55J, and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

Author : Vivek S. Borkar
Publisher : Longman
Page : 212 pages
File Size : 53,6 Mb
Release : 1989
Category : Control theory
ISBN : UCAL:B4405859

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Optimal Control of Diffusion Processes by Vivek S. Borkar Pdf

Author : N.V. Krylov
Publisher : Springer
Page : 0 pages
File Size : 51,6 Mb
Release : 2013-01-14
Category : Mathematics
ISBN : 1461260515

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Controlled Diffusion Processes by N.V. Krylov Pdf

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. During that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in W onham [76J). At the same time, Girsanov [25J and Howard [26J made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4J. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8J, Mine and Osaki [55J, and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

Author : Ari Arapostathis,Vivek S. Borkar,Mrinal K. Ghosh
Publisher : Cambridge University Press
Page : 341 pages
File Size : 44,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780521768405

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Ergodic Control of Diffusion Processes by Ari Arapostathis,Vivek S. Borkar,Mrinal K. Ghosh Pdf

The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.

Author : Helmut Mehrer
Publisher : Springer Science & Business Media
Page : 645 pages
File Size : 46,8 Mb
Release : 2007-07-24
Category : Technology & Engineering
ISBN : 9783540714880

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Diffusion in Solids by Helmut Mehrer Pdf

This book describes the central aspects of diffusion in solids, and goes on to provide easy access to important information about diffusion in metals, alloys, semiconductors, ion-conducting materials, glasses and nanomaterials. Coverage includes diffusion-controlled phenomena including ionic conduction, grain-boundary and dislocation pipe diffusion. This book will benefit graduate students in such disciplines as solid-state physics, physical metallurgy, materials science, and geophysics, as well as scientists in academic and industrial research laboratories.

Author : Wendell H. Fleming,Halil Mete Soner
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 44,5 Mb
Release : 2006-02-04
Category : Mathematics
ISBN : 9780387310718

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Controlled Markov Processes and Viscosity Solutions by Wendell H. Fleming,Halil Mete Soner Pdf

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Author : Gerd Infanger
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 45,6 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 9781441916426

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Stochastic Programming by Gerd Infanger Pdf

From the Preface... The preparation of this book started in 2004, when George B. Dantzig and I, following a long-standing invitation by Fred Hillier to contribute a volume to his International Series in Operations Research and Management Science, decided finally to go ahead with editing a volume on stochastic programming. The field of stochastic programming (also referred to as optimization under uncertainty or planning under uncertainty) had advanced significantly in the last two decades, both theoretically and in practice. George Dantzig and I felt that it would be valuable to showcase some of these advances and to present what one might call the state-of- the-art of the field to a broader audience. We invited researchers whom we considered to be leading experts in various specialties of the field, including a few representatives of promising developments in the making, to write a chapter for the volume. Unfortunately, to the great loss of all of us, George Dantzig passed away on May 13, 2005. Encouraged by many colleagues, I decided to continue with the book and edit it as a volume dedicated to George Dantzig. Management Science published in 2005 a special volume featuring the “Ten most Influential Papers of the first 50 Years of Management Science.” George Dantzig’s original 1955 stochastic programming paper, “Linear Programming under Uncertainty,” was featured among these ten. Hearing about this, George Dantzig suggested that his 1955 paper be the first chapter of this book. The vision expressed in that paper gives an important scientific and historical perspective to the book. Gerd Infanger

Author : Zhenting Hou,Jerzy A. Filar,Anyue Chen
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 40,7 Mb
Release : 2002-09-30
Category : Business & Economics
ISBN : 1402008031

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Markov Processes and Controlled Markov Chains by Zhenting Hou,Jerzy A. Filar,Anyue Chen Pdf

The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.

Author : Xi-Ren Cao
Publisher : Springer Nature
Page : 376 pages
File Size : 53,5 Mb
Release : 2020-05-13
Category : Technology & Engineering
ISBN : 9783030418465

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Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems by Xi-Ren Cao Pdf

This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.

Author : Radek Erban,S. Jonathan Chapman
Publisher : Cambridge University Press
Page : 321 pages
File Size : 54,9 Mb
Release : 2020-01-30
Category : Mathematics
ISBN : 9781108498128

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Stochastic Modelling of Reaction-Diffusion Processes by Radek Erban,S. Jonathan Chapman Pdf

Practical introduction for advanced undergraduate or beginning graduate students of applied mathematics, developed at the University of Oxford.

Author : Bernt Øksendal,Agnès Sulem
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 42,5 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9783540698265

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Applied Stochastic Control of Jump Diffusions by Bernt Øksendal,Agnès Sulem Pdf

Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Author : Harold Kushner
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244820

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Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by Harold Kushner Pdf

The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

Author : Harold J. Kushner,Paul Dupuis
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 43,9 Mb
Release : 2001
Category : Language Arts & Disciplines
ISBN : 0387951393

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold J. Kushner,Paul Dupuis Pdf

The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.

Author : Onesimo Hernandez-Lerma,Jean B. Lasserre
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207290

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Discrete-Time Markov Control Processes by Onesimo Hernandez-Lerma,Jean B. Lasserre Pdf

This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.