Selected Aspects of Fractional Brownian Motion
Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of i
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BOCCONI & SPRINGER SERIES Mathematics, Statistics, Finance and Economics
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Selected Aspects of Fractional Brownian Motion
To Lili, Juliette and Delphine
Series Editors: Sandro Salsa (Editor-in-Chief) Carlo A. Favero • Peter Müller • Lorenzo Peccati • Eckhard Platen • Wolfgang J. Runggaldier • Marc Yor
Ivan Nourdin
Selected Aspects of Fractional Brownian Motion
Ivan Nourdin Université de Lorraine Vandoeuvre-lès-Nancy France
ISSN 2039-1471 ISSN 2039-148X (electronic) B&SS – Bocconi & Springer Series ISBN 978-88-470-2822-7 ISBN 978-88-470-2823-4 (eBook) DOI 10.1007/978-88-470-2823-4 Springer Milan Heidelberg New York Dordrecht London Library of Congress Control Number: 2012945544 Mathematics Subject Classification: 60G15, 60H07, 60F05, 46L54 © Springer-Verlag Italia 2012 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. 9 8 7 6 5 4 3 2 1 Cover design: Beatrice B, Milano Typesetting: PTP-Berlin, Protago TEX-Production GmbH, Germany (www.ptp-berlin.de) Printing: Grafiche Porpora, Segrate (MI) Printed on acid-free paper Printed in Italy Springer-Verlag Italia S.r.l., Via Decembrio 28, I-20137 Milano Springer is a part of Springer Science+Business Media (www.springer.com)
Preface
As is well-known, the classical Brownian motion is a stochastic process which is selfsimilar of index 1/2 and has stationary increments. It is actually the only continuous Gaussia
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