Stochastic Control Theory Dynamic Programming Principle
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems.First we consider completely observable control problems with finite horizons.
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Makiko Nisio
Stochastic Control Theory Dynamic Programming Principle Second Edition
Probability Theory and Stochastic Modelling Volume 72
Editors-in-Chief Søren Asmussen, Aarhus, Denmark Peter W. Glynn, Stanford, CA, USA Thomas Kurtz, Madison, WI, USA Yves Le Jan, Paris, France Advisory Board Joe Gani, Canberra, Australia Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Andreas E. Kyprianou, Bath, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, Canada Halil Mete Soner, Zurich, Switzerland
The Stochastic Modelling and Probability Theory series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. 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 • • • • • •
Gaussian processes Markov processes Random Fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
Makiko Nisio
Stochastic Control Theory Dynamic Programming Principle
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Makiko Nisio (emeritus) Kobe University Kobe, Japan Osaka Electro–Communication University Osaka, Japan
First edition published in the series ISI Lecture Notes, No 9, by MacMillan India Limited publishers, c Makiko Nisio, 1981 Delhi,
ISSN 2199-3130 ISSN 2199-3149 (electronic) ISBN 978-4-431-55122-5 ISBN 978-4-431-55123-2 (eBook) DOI 10.1007/978-4-431-55123-2 Springer Tokyo Heidelberg New York Dordrecht London Library of Congress Control Number: 2014953914 Mathematics Subject Classification: 93E20, 60H15 © Springer Japan 2015 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 illustrations, recitation, broa
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