Almost Periodic Stochastic Processes
Almost Periodic Stochastic Processes is among the few published books that is entirely devoted to almost periodic stochastic processes and their applications. The topics treated range from existence, uniqueness, boundedness, and stability of solutio
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Paul H. Bezandry • Toka Diagana
Almost Periodic Stochastic Processes
Paul H. Bezandry Department of Mathematics Howard University 2441 6th Street NW 20059 Washington District of Columbia USA [email protected]
Toka Diagana Department of Mathematics Howard University 2441 6th Street NW 20059 Washington District of Columbia USA [email protected]
ISBN 978-1-4419-9475-2 e-ISBN 978-1-4419-9476-9 DOI 10.1007/978-1-4419-9476-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011925256 Mathematics Subject Classification (2010): 34K50, 34K30, 35R60, 39A24, 39A50, 47D06, 60-XX, 60Axx, 65J08
© Springer Science+Business Media, LLC 2011 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)
To our families
Acknowledgments
We would like to thank our wives and kids for support and encouragement. Their patience and encouragement have made everything possible including this book. We wish to thank members of the Howard University’s Mathematics Department as well as the College of Arts & Sciences for their strong support since both of us joined Howard University ten years ago. We are grateful to Professors Terrence Mills and Alexander Pankov for proofreading all the versions of this book. Their comments and suggestions have significantly improved this book. Our sincerest gratitude goes to both of them. We are grateful to Springer for agreeing to publish our book. Additionally, we would like to express our deepest gratitude to the reviewer for careful reading of the book and insightful comments.
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Preface
This book analyzes almost periodic stochastic processes and their applications to various stochastic differential equations, partial differential equations, and difference equations. It is in part a sequel the of authors’ recent work [20, 21, 22, 23, 24, 55] on almost periodic stochastic difference and differential equations and has the particularity to be among the few books that are entirely devoted to almost periodic stochastic processes and their applications. The topics treated in it range from existence, uniqueness, boundedness, and stability of solutions to stochastic difference and differential equations. Periodicity often appears in implicit ways in various natural phenomena. For instance, this is the case when o
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