Continuous-Time Markov Decision Processes

Alexey Piunovskiy was born in Moscow, USSR, in 1954. He obtained his PhD in 1981 from the Moscow State Institute of Electronics and Mathematics, and his DSc from the Moscow State Institute of Physics and Technology in 2000. Since then he has been at the University of Liverpool, where he is presently a Reader. His research interests include stochastic optimal control and constrained optimization.  Yi Zhang was born in Qingdao, PRC, in 1985. He obtained his PhD in 2010 from the Department of Mathematical Sciences at the University of Liverpool, where he is currently a Lecturer. His research interests include stochastic models in operational research, Markov decision processes and their applications to problems in statistics and optimal control.

“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)

• Foreword.- Preface.- Description of CTMDPs and Preliminaries.- Selected Properties of Controlled Processes.- The Discounted Cost Model.- Reduction to DTMDP: The Total  Cost Model.- The Average Cost Model.- The Total Cost Model: General Case.- Gradual-Impulsive Control Models.- Appendices: Miscellaneous Results.-Relevant Definitions and Facts.- Definitions and Facts about Discrete-Time Markov Decision Processes.- Bibliography.- Index.- Notation.