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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.

Stochastic control theory. --- Hamilton-Jacobi equations. --- Equations, Hamilton-Jacobi --- Equations, Jacobi-Hamilton --- Jacobi-Hamilton equations --- Calculus of variations --- Differential equations, Partial --- Hamiltonian systems --- Mechanics --- Control theory --- Stochastic processes --- Distribution (Probability theory. --- Differential equations, partial. --- Mathematical statistics. --- Probability Theory and Stochastic Processes. --- Partial Differential Equations. --- Control, Robotics, Mechatronics. --- Statistical Theory and Methods. --- Partial differential equations --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods --- Probabilities. --- Partial differential equations. --- Control engineering. --- Robotics. --- Mechatronics. --- Statistics . --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Machine theory