Numerical Methods for Controlled Stochastic Delay Systems

- Preface

- Introduction

- Stochastic Models

- Mathematical Background

- Properties of and Approximations to Stochastic Delay Equations

- The Ergodic Cost Problem: Mathematical Background

- Introduction to the Markov Chain Approximation Method

- Markov Chain Approximation Path Only Delayed

- Markov Chain Approximations: Control, Reflection Term, and/or Wiener Process Also Delayed

- The Ergodic Cost Problem

- Numerical Algorithms for Solving the Markov Chian Approximation Control Problems

- 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 stochastic control problems in continuous time to stochastic systems with delays which arise in the realistic modeling of many physical, mechanical, biological or medical systems. ... An Index, a Symbol Index and a 95 titles reference list are also provided. ... used as a graduate level textbook or as a reference for researchers or practitioners dealing with stochastic delay equations, and interested in either the use of algorithms or of the underlying mathematics." (Adriana-Ioana Lefter, Memoirs of the Scientific Sections, 2009)

"The book deals with numerical methods for nonlinear continuous time stochastic control systems with delays. ... The book appears of particular importance for the practical solution to stochastic control problems for systems with delays. ... it does not contain only results, but also ideas and suggestions so that it can be considered as an important source of inspiration for further work in this field." (Giovanni Di Masi, Zentralblatt MATH, Vol. 1219, 2011)