Sharp Martingale and Semimartingale Inequalities
This monograph presents a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in
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M a t e ma t y c z n e
Instytut Matematyczny Polskiej Akademii Nauk (IMPAN)
Volume 72 (New Series) Founded in 1932 by S. Banach, B. Knaster, K. Kuratowski, S. Mazurkiewicz, W. Sierpinski, H. Steinhaus
Managing Editor: Marek Bozejko (Wroclaw University, Poland) Editorial Board: Jean Bourgain (IAS, Princeton, USA) Joachim Cuntz (University of Münster, Germany) Ursula Hamenstädt (University of Bonn, Germany) Gilles Pisier (Texas A&M University, USA) Piotr Pragacz (IMPAN, Poland) Andrew Ranicki (University of Edinburgh, UK) Slawomir Solecki (University of Illinois, Urbana-Champaign, USA) Przemyslaw Wojtaszczyk (IMPAN and Warsaw University, Poland) Jerzy Zabczyk (IMPAN, Poland) Henryk Zoladek (Warsaw University, Poland)
Volumes 31–62 of the series Monografie Matematyczne were published by PWN – Polish Scientific Publishers, Warsaw
Adam Osękowski
Sharp Martingale and Semimartingale Inequalities
Adam OsĊkowski Institute of Mathematics University of Warsaw Warsaw Poland
ISBN 978-3-0348-0369-4 ISBN 978-3-0348-0370-0 (eBook) DOI 10.1007/978-3-0348-0370-0 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2012945527
Mathematics Subject Classification (2010): Primary: 60G42, 60G44, 60G46; secondary: 31B05, 31B20, 42B25, 46B20, 46C15 © Springer Basel 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. Printed on acid-free pape
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