Sample Path Analysis and Distributions of Boundary Crossing Times
This monograph is focused on the derivations of exact distributions of first boundary crossing times of Poisson processes, compound Poisson processes, and more general renewal processes. The content is limited to the distributions of first boundary
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Shelemyahu Zacks
Sample Path Analysis and Distributions of Boundary Crossing Times
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zürich Alessio Figalli, Zürich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Shelemyahu Zacks
Sample Path Analysis and Distributions of Boundary Crossing Times
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Shelemyahu Zacks Binghamton University Binghamton, NY, USA
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-67058-4 ISBN 978-3-319-67059-1 (eBook) https://doi.org/10.1007/978-3-319-67059-1 Library of Congress Control Number: 2017952339 Mathematics Subject Classification (2010): 60-02, 60-K15, 60-K20, 60-K40 © Springer International Publishing AG 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my wife Hanna with love
Preface
The material presented in this manuscript was developed for different applications and published in many papers which are listed among the references. My colleagues recommended that I gather all this material into one manuscript, to have it readily available to students and researchers in applied probability. The Lecture Notes series is an appropriate location for such a project. I wrote first a draft which I gave to several colleagues to read and provide comments. I then revised the manuscript accordingly. I hope this manuscript is helpful to students and researchers in differe
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