Continuous-Time Markov Decision Processes
Borel Space Models and General Control Strategies
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Beschreibung
This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies.
Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth.
The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail.
Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.
This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies.
Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth.
The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail.
Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.
Features a detailed treatment of constrained problems Covers exponential semi-Markov decision processes Includes various unpublished results and illustrates the theory with new solved examples Introduces new and broad classes of strategies
Autor*in
Alexey Piunovskiy
Themen in »Continuous-Time Markov Decision Processes«
90C40, 60J75 continuous-time Markov decision processes dynamic programming convex analytic approach linear programming occupation measure constrained optimality Markov pure jump processes statistical decision theory sequential analysis stochastic optimal control
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“This book is a complete treatise on continuous-time Markov decision processes (CTMDPs) on Borel spaces … . The theory presented is developed in a careful and detailed form. Moreover, several examples and applications are given. Therefore, the book is interesting from both the theoretical and applied points of view. … It is important to mention that at the end of each chapter, bibliographical remarks are supplied which complement and clarify the information given in it.” (Raúl Montes-de-Oca, Mathematical Reviews, April, 2022)
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