Numerical Methods for Controlled Stochastic Delay Systems [Hardcover]

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. The 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 either in the use of the algorithms or in the 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.

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. It is the first book on the subject.

PrefaceExamples and IntroductionWeak Convergence and MartingalesStochastic Delay Equations: ModelsApproximations to the Dynamical ModelsThe Ergodic Cost ProblemMarkov Chain Approximations: IntroductionMarkov Chain Approximations: Path and Control DelayedPath and Control Delayed: ContinuedA Wave Equation ApproachReferencesIndexSymbol Index

From the reviews:

Overall this is a book entirely devoted to numerics of controlled stochastic systems with delays. In addition to analysis, it contains many numerical and simulation results. The book should be beneficial to both people working in the numerical methods of stochastic controls and people working in various applications who need to use numerical algorithms. It is perhaps the only comprehensive numerical study of controlled diffusions with delays to date...[I]t is conceivable that this book will become a standard reference in the stochastic control literature. ?? Mathematical Reviews

This book extends the Markov chain approximation methods from nonlinear stochastil_