Numerical Methods for Stochastic Control Problems in Continuous Time / Edition 2

by Harold Kushner, Paul G. Dupuis

Overview

Changes in the second edition. The second edition differs from the first in that there is a full development of problems where the variance of the diffusion term and the jump distribution can be controlled. Also, a great deal of new material concerning deterministic problems has been added, including very efficient algorithms for a class of problems of wide current interest. This book is concerned with numerical methods for shastic control and optimal shastic control problems. The random process models of the controlled or uncontrolled shastic systems are either diffusions or jump diffusions. Shastic control is a very active area of research and new problem formulations and sometimes surprising applications appear regu­ larly. We have chosen forms of the models which cover the great bulk of the formulations of the continuous time shastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin­ uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types.

Product Details

ISBN-13:	9781461265313
Publisher:	Springer New York
Publication date:	11/27/2013
Series:	Stochastic Modelling and Applied Probability , #24
Edition description:	2nd ed. 2001. Softcover reprint of the original 2nd ed. 2001
Pages:	476
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Review of Continuous Time Models.- Controlled Markov Chains.- Dynamic Programming Equations.- Markov Chain Approximation Method.- The Approximating Markov Chains.- Computational Methods.- The Ergodic Cost Problem.- Heavy Traffic and Singular Control.- Weak Convergence and the Characterization of Processes.- Convergence Proofs.- Convergence Proofs Continued.- Finite Time and Filtering Problems.- Controlled Variance and Jumps.- Problems from the Calculus of Variations: Finite Time Horizon.- Problems from the Calculus of Variations: Infinite Time Horizon.- The Viscosity Solution Approach.

Editorial Reviews

Process models used are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. The required background in stochastic processes is surveyed, followed by extensive development of methods of approximation and a chapter devoted to computational techniques. The book is written on two levels, that of algorithms and applications, and that of mathematical development, making the methods used broadly accessible. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"The second edition of this acclaimed book from Springer-Verlag has the latest theoretical and practical information on solving shastic control problems. Including proofs and algorithms using diffusion, jump-diffusion, and other process models, the authors help make randomness a little less scary."

Amazon.com Delivers Mathematics and Statistics e-bulletin, July 2001

From the Publisher