The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. Because such problems are infinite-dimensional, many new issues arise in getting good numerical approximations and in the convergence proofs. Useful forms of numerical algorithms and system approximations are developed in this work, and the convergence proofs are given. All of the usual cost functions are treated as well as singular and impulsive controls. A major concern is on representations and approximations that use minimal memory. Featuring numerical algorithms and examples with applications to control and modern communications systems, this book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is in either the use of the algorithms or in the underlying mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.
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