Numerical Methods for Stochastic Control Problems in Continuous Time: v. 24 (Applications of Mathematics) - Hardcover

Kushner, Harold J.; Dupuis, Paul

9783540978343: Numerical Methods for Stochastic Control Problems in Continuous Time: v. 24 (Applications of Mathematics)

Hardcover

ISBN 10: 3540978348 ISBN 13: 9783540978343

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

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The text presents a comprehensive development of effective numberical 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. Convergence o f the numberical approximations is proved via the efficient probabilistic methods of weak convergence theory. The methods also apply to the calculation of functionals of uncontrolled processes and for the appropriate to optimal nonlinear filters as well. 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. Essentially all that is required of the approximations are some natural local consistency conditions. The approximations are consistent with standard methods of numerical analysis. The required background in 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.

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Review

"The second edition of this acclaimed book from Springer-Verlag has the latest theoretical and practical information on solving stochastic 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

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