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Overview
Shastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for shastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Synopsis
This book presents a comprehensive development of effective numerical methods for stochastic control problems in continuous time. The process models are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. All the usual problem formulations are included, as well as those of more recent interest such as ergodic control, singular control and the types of reflected diffusions used as models of queuing networks. Applications to complex deterministic problems are illustrated via application to a large class of problems from the calculus of variations. The general approach is known as the Markov Chain Approximation Method. The required background to stochastic processes is surveyed, there is an extensive development of methods of approximation, and a chapter is devoted to computational techniques. The book is written on two levels, that of practice (algorithms and applications) and that of the mathematical development. Thus the methods and use should be broadly accessible. This update to the first edition will include added material on the control of the 'jump term' and the 'diffusion term.' There will be additional material on the deterministic problems, solving the Hamilton-Jacobi equations, for which the authors' methods are still among the most useful for many classes of problems. All of these topics are of great and growing current interest.
Booknews
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)