Potential Analysis of Stable Processes and its Extensions
Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with r
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1980
Krzysztof Bogdan · Tomasz Byczkowski Tadeusz Kulczycki · Michal Ryznar Renming Song · Zoran Vondraˇcek
Potential Analysis of Stable Processes and its Extensions Volume Editors: Piotr Graczyk Andrzej Stos
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Editors Piotr Graczyk
Andrzej Stos
LAREMA Université d’Angers 2 bd Lavoisier 49045 Angers France [email protected]
Laboratoire de Mathématiques Université Blaise Pascal Campus Universitaire des Cézeaux 63177 Aubière France [email protected]
Authors: see List of Contributors
ISBN: 978-3-642-02140-4 DOI: 10.1007/978-3-642-02141-1
e-ISBN: 978-3-642-02141-1
Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2009928106 Mathematics Subject Classification (2000): 60J45, 60G52, 60J50, 60J75, 31B25, 31C05, 31C35, 31C25 c Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: SPi Publisher Services Printed on acid-free paper springer.com
Foreword
This monograph is devoted to the potential theory of stable stochastic processes and related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schr¨ odinger operators. The stable L´evy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics, and the theoretical motivation for the study of their fine properties is also very strong. The potential theory of stable and related processes naturally extends the theory established in the classical case of the Brownian motion and the Laplace operator. The foundations and general setting of probabilistic potential theory were given by G.A. Hunt [92](1957), R.M. Blumenthal and R.K. Getoor [23](1968), S.C. Port and J.C. Stone [130](1971). K.L. Chung and Z. Zhao [62](1995) have studied the potential theory of the Brownian motion and related Schr¨ odinger operators. The present book focuses on classes of processes that contain the Brownian motion as a special case. A part of this volume may also be viewed as a probabilistic counterpart of the book of N.S. Landkof [117](1972). The main part of Introduction that open
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