Stable Non-Gaussian Self-Similar Processes with Stationary Increments
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called det
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Vladas Pipiras Murad S. Taqqu
Stable Non-Gaussian Self-Similar Processes with Stationary Increments
123
SpringerBriefs in Probability and Mathematical Statistics Editor-in-chief Mark Podolskij, Aarhus C, Denmark Series editors Nina Gantert, M¨unster, Germany Richard Nickl, Cambridge, UK Sandrine P´ech´e, Paris, France Gesine Reinert, Oxford, UK Mathieu Rosenbaum, Paris, France Wei Biao Wu, Chicago, USA
More information about this series at http://www.springer.com/series/14353
Vladas Pipiras • Murad S. Taqqu
Stable Non-Gaussian Self-Similar Processes with Stationary Increments
123
Vladas Pipiras Statistics and Operations Research University of North Carolina at Chapel Hill Chapel Hill, NC, USA
Murad S. Taqqu Department of Mathematics and Statistics Boston University Boston, MA, USA
ISSN 2365-4333 ISSN 2365-4341 (electronic) SpringerBriefs in Probability and Mathematical Statistics ISBN 978-3-319-62330-6 ISBN 978-3-319-62331-3 (eBook) DOI 10.1007/978-3-319-62331-3 Library of Congress Control Number: 2017947156 © The Author(s) 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 Terese, Jovita, and Milda and to Jeremy and Yael
Preface
Fractional Brownian motion is (up to a constant and for a fixed self-similarity parameter) the unique Gaussian self-similar process with stationary increments. When the assumption of Gaussian distributions is replaced by that of stable (non-Gaussian) distributions, the situation is more complex. This is because there are in fact many different such stable (non-Gaussian) processes (this is for the same self-similarity and stability parameters, discounting multiplicative constants). This work pro
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