Quantum Independent Increment Processes I From Classical Probability
This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg
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David Applebaum B.V. Rajarama Bhat Johan Kustermans J. Martin Lindsay
Quantum Independent Increment Processes I From Classical Probability to Quantum Stochastic Calculus
Editors: Michael Sch¨urmann Uwe Franz
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Editors and Authors David Applebaum Probability and Statistics Department University of Sheffield Hicks Building Hounsfield Road Sheffield, S3 7RH, UK E-mail: D.Applebaum@sheffield.ac.uk
Johan Kustermans KU Leuven Department Wiskunde Celestijnenlaan 200B 3001 Heverlee, Belgium E-mail: [email protected]
B.V. Rajarama Bhat Indian Statistical Institute 8th Mile, Mysore Road Bangalore 560 059, India
J. Martin Lindsay School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD, UK
E-mail: [email protected]
E-mail: [email protected]
Uwe Franz Inst. Mathematik und Informatik Universit¨at Greifswald Friedrich-Ludwig-Jahn-Str. 15a 17487 Greifswald, Germany
Michael Sch¨urmann Inst. Mathematik und Informatik Universit¨at Greifswald Friedrich-Ludwig-Jahn-Str. 15a 17487 Greifswald, Germany
E-mail: [email protected]
E-mail: [email protected]
Library of Congress Control Number: 2004117328
Mathematics Subject Classification (2000): 60G51, 81S25, 46L60, 58B32, 47A20, 16W30 ISSN 0075-8434 ISBN 3-540-24406-9 Springer-Verlag Berlin Heidelberg New York DOI 10.1007/b105131 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm 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-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag is a part of Springer Science + Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors 41/3142/du - 543210 - Printed on acid-free paper
Dedicated to the memory of Paul-Andr´e Meyer
Preface
This volume is the first of two volumes containing the lectures given at the School “Quantum Independent Increment Processes: Structure and Applications to Physics”. This school was held at the Alfried Krupp Wissenschafts}kolleg in Greifswald during the period March 9 – 22, 2003. We thank the lecturers for all the hard work they accomplished. Their lectures give an introduction to current research in their domains that is accessible to Ph. D. students. We hope that the two volumes will help to bring researchers from the
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