Hybrid Switching Diffusions Properties and Applications
This book presents a comprehensive study of hybrid switching diffusion processes and their applications. The motivations for studying such processes originate from emerging and existing applications in wireless communications, signal processing, queueing
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Stochastic Modelling and Applied Probability (Formerly: Applications of Mathematics)
63
Edited by B. Rozovski˘ı G. Grimmett Advisory Board D. Dawson D. Geman I. Karatzas F. Kelly Y. Le Jan B. Øksendal G. Papanicolaou E. Pardoux
For other titles in this series, go to http://www.springer.com/series/602
G. George Yin • Chao Zhu
Hybrid Switching Diffusions Properties and Applications
G. George Yin Department of Mathematics Wayne State University Detroit, MI 48202 USA [email protected]
Chao Zhu Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, WI 53201 USA [email protected]
Managing Editors Boris Rozovski˘ı Division of Applied Mathematics Brown University 182 George St Providence, RI 02912 USA [email protected]
Geoffrey Grimmett Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB UK [email protected]
ISSN 0172-4568 ISBN 978-1-4419-1104-9 e-ISBN 978-1-4419-1105-6 DOI 10.1007/978-1-4419-1105-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009934520 Mathematics Subject Classification (2000): 60J27, 60J60, 93E03, 93E15 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
In memory of my sister Kewen Yin, who taught me algebra, calculus, physics, and chemistry during the Cultural Revolution, when I was working in a factory in Beijing and she was over 1000 miles away at a factory in Lanzhou George Yin
To my parents Yulan Zhong and Changming Zhu and my wife Lijing Sun, with love Chao Zhu
Contents
Preface
xi
Conventions
xv
Glossary of Symbols 1 Introduction and Motivation 1.1 Introduction . . . . . . . . . . . . 1.2 Motivation . . . . . . . . . . . . 1.3 What Is a Switching Diffusion . . 1.4 Examples of Switching Diffusions 1.5 Outline of the Book . . . . . . .
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Part I: Basic Properties, Recurrence, Ergodicity 2 Switching Diffusion 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Switching Diffusions . . . . . . . . . . . . . . . . . . . . . 2.3 Regularity . . . . . . . . . . . . . . . . . .
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