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© 2008

Stochastic Control of Hereditary Systems and Applications

  • Mou-Hsiung Chang
Book

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 59)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Pages 79-125
  3. Pages 203-244
  4. Pages 245-292
  5. Pages 293-331
  6. Back Matter
    Pages 393-406

About this book

Introduction

This research monograph develops the Hamilton-Jacobi-Bellman (HJB) theory through dynamic programming principle for a class of optimal control problems for stochastic hereditary differential systems. It is driven by a standard Brownian motion and with a bounded memory or an infinite but fading memory.

The optimal control problems treated in this book include optimal classical control and optimal stopping with a bounded memory and over finite time horizon.

This book can be used as an introduction for researchers and graduate students who have a special interest in learning and entering the research areas in stochastic control theory with memories. Each chapter contains a summary.

Mou-Hsiung Chang is a program manager at the Division of Mathematical Sciences for the U.S. Army Research Office.

Keywords

Applications Brownian motion Chang Control Hereditary Stochastic Stochastic calculus

Editors and affiliations

  • Mou-Hsiung Chang
    • 1
  1. 1.U.S. Army Research OfficeDurhamUSA

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Reviews

From the reviews:

"A large class of models from physics, chemistry … etc., is described by stochastic hereditary differential equations (SHDEs) driven by a standard Brownian motion. … The monograph is addressed to researchers and advanced graduate students with interest in the theory and applications of optimal control for SHDEs. … The monograph provides a systematic and careful exposition of the fundamental results of the control problems for stochastic hereditary differential systems and represents an essential source of information for anyone who wants to work in the field." (Constantin Tudor, Mathematical Reviews, Issue 2009 e)

“The theme of this research monograph is a set of equations that represent a class of infinite-dimensional stochastic systems. … This monograph can serve as an introduction and/or a research reference for researchers and advanced graduate students with a special interest in theory and applications of optimal control of SHDEs. The monograph is intended to be as self-contained as possible. … Theory developed in this monograph can be extended with additional efforts to hereditary differential equations driven by semimartingales, such as Lévy processes.” (Adriana Horníková, Technometrics, Vol. 52 (2), May, 2010)