About this book
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.
Editors and affiliations
- Book Title Stochastic Control of Hereditary Systems and Applications
- Series Title Stochastic Modelling and Applied Probability
- DOI https://doi.org/10.1007/978-0-387-75816-9
- Copyright Information Springer New York 2008
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-0-387-75805-3
- Softcover ISBN 978-1-4419-2605-0
- eBook ISBN 978-0-387-75816-9
- Series ISSN 0172-4568
- Edition Number 1
- Number of Pages XVIII, 406
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Probability Theory and Stochastic Processes
Partial Differential Equations
Control, Robotics, Mechatronics
Statistical Theory and Methods
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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)