High Magnetic Fields : Science And Technology. Volume 1, Magnet Technology Anbd Experimental Techniques

Quantum probability communications This page is intentionally left blank QP-PQ Volume XI Quantum probability communications Managing Editors Stephane Attal, J. Martin Lindsay Editorial Board Ph. Biane, F. Fagnola, M. Fannes, B. Kummerer, H. Maassen, D. Petz Advisory Board L. Accardi, L. Gross, T. Hida, K. R. Parthasarathy, A. Verbeure, D. Voiculescu V f e World Scientific wll Si New Jersey • London • Singapore • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. QUANTUM PROBABILITY COMMUNICATIONS, VOL. XI Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-238-976-8 ISBN 981-238-975-X(pbk) ISBN 981-238-427-8 ISBN 981-238-428-6 (pbk) Printed in Singapore. CONTENTS Contents of QPC XII vi Preface for Volumes XI & XII vii Extensions of quantum stochastic calculus Stephane Attal 1 Quantum Ito algebras: axioms, representations, decompositions Viacheslav Belavkin 39 Free probability for probabilists Philippe Biane 55 Conditional expectations on von Neumann algebras 73 Carlo Cecchini Classical probability theory: an outline of stochastic integrals and diffusions Michel Emery 87 Quantum stochastic differential equations 123 Franco Fagnola Canonical commutation and anticommutation relations Mark Fannes 171 Quantum and classical stochastic calculus Alexander Holevo 199 An introduction to quantum stochastic calculus and some of its applications Robin Hudson 221 Stationary processes in quantum probability 273 Burkhard Kummerer v CONTENTS of Q P C XII Integral-sum kernel operators J. Martin Lindsay 1 Quantum probability applied to the damped harmonic oscillator Hans Maassen 23 Quantum probability and strong quantum Markov processes K. R. Parthasarathy 59 Limit problems for quantum dynamical semigroups — inspired by scattering theory 139 Rolando Rebolledo A survey of operator algebras Jean-Luc Sauvageot 173 Quantum stop times Kalyan B. Sinha 195 Free calculus Roland Speicher 209 Continuous kernel processes in quantum probability Wilhelm von Wa