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Ole E. Barndorff-Nielsen · Uwe Franz · Rolf Gohm Burkhard Kümmerer · Steen Thorbjørnsen

Quantum Independent Increment Processes II Structure of Quantum Lévy Processes, Classical Probability, and Physics Editors: Michael Schüermann Uwe Franz

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Editors and Authors Ole E. Barndorff-Nielsen Department of Mathematical Sciences University of Aarhus Ny Munkegade, Bldg. 350 8000 Aarhus Denmark e-mail: [email protected]

Burkhard Kümmerer Fachbereich Mathematik Technische Universität Darmstadt Schlossgartenstr. 7 64289 Darmstadt Germany e-mail: kuemmerer@mathematik. tu-darmstadt.de

Michael Schuermann Rolf Gohm Uwe Franz Institut für Mathematik und Informatik Universität Greifswald Friedrich-Ludwig-Jahn-Str. 15a 17487 Greifswald Germany e-mail: [email protected] [email protected] [email protected]

Steen Thorbjørnsen Department of Mathematics and Computer Science University of Southern Denmark Campusvej 55 5230 Odense Denmark e-mail: [email protected]

Library of Congress Control Number: 2005934035 Mathematics Subject Classification (2000): 60G51, 81S25, 46L60, 58B32, 47A20, 16W30 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-24407-7 Springer Berlin Heidelberg New York ISBN-13 978-3-540-24407-3 Springer Berlin Heidelberg New York DOI 10.1007/11376637 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006
Printed in The Netherlands 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. Typesetting: by the authors and Techbooks using a Springer LATEX package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper

SPIN: 11376637

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Preface

This volume is the second 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 Wissenschaftskolleg 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 areas of classical and quant