Selected Properties of Controlled Processes
The main purpose of this chapter is to present some properties of the controlled processes that are closely related to the optimal control problems considered in this book. In Sect. 2.1 , we rigorously show that under a natural Markov strategy \(\breve{\p
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Alexey Piunovskiy Yi Zhang
Continuous-Time Markov Decision Processes Borel Space Models and General Control Strategies
Probability Theory and Stochastic Modelling Volume 97
Editors-in-Chief Peter W. Glynn, Stanford, CA, USA Andreas E. Kyprianou, Bath, UK Yves Le Jan, Orsay, France Advisory Editors Søren Asmussen, Aarhus, Denmark Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series, Stochastic Modelling and Applied Probability and Probability and Its Applications. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students, as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
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Alexey Piunovskiy Yi Zhang •
Continuous-Time Markov Decision Processes Borel Space Models and General Control Strategies
Foreword by Albert Nikolaevich Shiryaev
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Alexey Piunovskiy Department of Mathematical Sciences University of Liverpool Liverpool, UK
Yi Zhang Department of Mathematical Sciences University of Liverpool Liverpool, UK
ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-3-030-54986-2 ISBN 978-3-030-54987-9 (eBook) https://doi.org/10.1007/978-3-030-54987-9 Mathematics Subject Classification: 90C40, 60J76, 62L10, 90C05, 90C29, 90C39, 90C46, 93C27, 93E20 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustra
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