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 areinfinite-dimensional, many new issues arise in getting good numerical approximations. Useful forms of the numerical algorithms and system approximations are developed and the convergence proofs are given. The necessary ergodic theoryis developed for the average cost per unit time problem. All of the usual cost functions are treated as well as singular and impulsive controls. A major concern in all cases is with representations and approximations that use minimalmemory. The book is the first on the subject and will be of great interest toall those who work with stochastic delay equations and whose main interest iseither in the use of the algorithms or in the mathematics. First book on the subject Various examples are presented with applications to control, biological modeling, and modern communications Main focus is on the development of conveniently programmed, intuitive, and robust algorithms that have good numericalproperties For a broad audience of graduate students, researchers, and practitioners in stochastic systems and communications INDICE: Preface.- Examples and Introduction.- Weak Convergence and Martingales.- Stochastic Delay Equations: Models.- Approximations to the Dynamical Models.- The Ergodic Cost Problem.- Markov Chain Approximations: Introduction.- Markov Chain Approximations: Path and Control Delayed.- Path and Control Delayed, Continued.- A Wave Equation Approach.- Subject Index.- Symbol Index.- References.
- ISBN: 978-0-8176-4534-2
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 300
- Fecha Publicación: 01/06/2008
- Nº Volúmenes: 1
- Idioma: Inglés