Optimal Control Of Diffusion Processes
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Author |
: N. V. Krylov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 314 |
Release |
: 2008-09-26 |
ISBN-10 |
: 9783540709145 |
ISBN-13 |
: 3540709142 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Controlled Diffusion Processes by : N. V. Krylov
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 |
: Xi-Ren Cao |
Publisher |
: Springer Nature |
Total Pages |
: 376 |
Release |
: 2020-05-13 |
ISBN-10 |
: 9783030418465 |
ISBN-13 |
: 3030418464 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems by : Xi-Ren Cao
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 |
: Wendell H. Fleming |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 231 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461263807 |
ISBN-13 |
: 1461263808 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Deterministic and Stochastic Optimal Control by : Wendell H. Fleming
This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.
Author |
: Bernt Øksendal |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 263 |
Release |
: 2007-04-26 |
ISBN-10 |
: 9783540698265 |
ISBN-13 |
: 3540698264 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Applied Stochastic Control of Jump Diffusions by : Bernt Øksendal
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 |
: Wendell H. Fleming |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 436 |
Release |
: 2006-02-04 |
ISBN-10 |
: 9780387310718 |
ISBN-13 |
: 0387310711 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Controlled Markov Processes and Viscosity Solutions by : Wendell H. Fleming
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 |
: Ari Arapostathis |
Publisher |
: Cambridge University Press |
Total Pages |
: 341 |
Release |
: 2012 |
ISBN-10 |
: 9780521768405 |
ISBN-13 |
: 0521768403 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Ergodic Control of Diffusion Processes by : Ari Arapostathis
The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.
Author |
: Gopinath Kallianpur |
Publisher |
: OUP Oxford |
Total Pages |
: 368 |
Release |
: 2014-01-09 |
ISBN-10 |
: 9780191004520 |
ISBN-13 |
: 0191004529 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Stochastic Analysis and Diffusion Processes by : Gopinath Kallianpur
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
Author |
: Vivek S. Borkar |
Publisher |
: Longman |
Total Pages |
: 212 |
Release |
: 1989 |
ISBN-10 |
: UCAL:B4405859 |
ISBN-13 |
: |
Rating |
: 4/5 (59 Downloads) |
Synopsis Optimal Control of Diffusion Processes by : Vivek S. Borkar
Author |
: Xungjing Li |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 462 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461242604 |
ISBN-13 |
: 1461242606 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Optimal Control Theory for Infinite Dimensional Systems by : Xungjing Li
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.
Author |
: Martin Lee Puterman |
Publisher |
: |
Total Pages |
: 100 |
Release |
: 1972 |
ISBN-10 |
: STANFORD:36105046359167 |
ISBN-13 |
: |
Rating |
: 4/5 (67 Downloads) |
Synopsis On the Optimal Control of Diffusion Processes by : Martin Lee Puterman
The author considers three problems in the optimal control of diffusion processes. The first is that of optimally controlling a diffusion process on a compact interval. The second problem is that of optimally controlling a diffusion process on a bounded subset of Euclidean n-space, with refledtion on the boundary. The last problem arises in controlling a continuous time production process. (Author).