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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

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Statistical science --- Partial differential equations --- Operational research. Game theory --- Applied physical engineering --- procesautomatisering --- differentiaalvergelijkingen --- stochastische analyse --- kansrekening --- regeltechniek --- statistisch onderzoek

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This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infi nite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.

Information theory. --- Channel Capacities. --- Memory Quantum Channels. --- Quantum Entanglement. --- Quantum Entropies. --- Quantum States.

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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.

Statistical science --- Partial differential equations --- Operational research. Game theory --- Applied physical engineering --- procesautomatisering --- differentiaalvergelijkingen --- stochastische analyse --- kansrekening --- regeltechniek --- statistisch onderzoek