Stochastic Control of Hereditary Systems and Applications

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.