Renewal Theory for Perturbed Random Walks and Similar Processes
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomen
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Alexander Iksanov
Renewal Theory for Perturbed Random Walks and Similar Processes
Probability and Its Applications
Series editors Steffen Dereich Davar Khoshnevisan Andreas Kyprianou Sidney I. Resnick
More information about this series at http://www.springer.com/series/4893
Alexander Iksanov
Renewal Theory for Perturbed Random Walks and Similar Processes
Alexander Iksanov Faculty of Computer Science and Cybernetics Taras Shevchenko National University of Kyiv Kyiv, Ukraine
ISSN 2297-0371 Probability and Its Applications ISBN 978-3-319-49111-0 DOI 10.1007/978-3-319-49113-4
ISSN 2297-0398 (electronic) ISBN 978-3-319-49113-4 (eBook)
Library of Congress Control Number: 2016961210 Mathematics Subject Classification (2010): 60-02, 60G, 60K © Springer International Publishing AG 2016 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, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my family
Preface
The present book offers a detailed treatment of perturbed random walks, perpetuities, and random processes with immigration. These objects are of major importance in modern probability theory, both theoretical and applied. Furthermore, these have been used to model various phenomena. Areas of possible applications include most of the natural sciences as well as insurance and finance. Recent years have seen an explosion of activity around perturbed random walks, perpetuities, and random processes with immigration. Over the last decade, several nice results have been proved, and some efficient techniques and methods have been worked out. This book is a result of a growing author’s conviction that the time has come to present in a book format main developments in the area accumulated to date. Summarizing, the first purpose of this book is to provide a thorough discussion of
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