Diffusion Processes and Related Problems in Analysis, Volume II Stoc
During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a
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Diffusion Processes and Related Problems in Analysis, Volume II Stochastic Flows Mark A. Pinsky Volker Wihstutz Editors
Springer Science+Business Media, LLC
Mark A. Pinsky
Department of Mathematics Northwestern University Evanston, IL 60208
Volker Wihstutz Department of Mathematics University of North Carolina Charlotte, N.C. 28223
Library of Congress Cata1oging-in-Publication Data Diffusion processes and related problems in analysis. (Progress in probability ; 22, 27) Papers presented al an international conference held October 23-27,1989 and sponsored by the Mathematics Department of Northwestem University. VoI. 2- edited by Mark Pinsky, Volker Wihstutz. Includes bibliographical references. Contents: v. 1. Diffusions in analysis and geometry -- v. 2. Stochastic flows. 1. Diffusion processes--Congresses. 2. Stochastic analysis--Congresses. 1. Pinsky, Mark A., 1940ll. Wihstutz, V. (Volker), 1940ill. Northwestem University (Evanston. DI.). Dept. of Mathematics. IV. Series: Progress in probability ; 22, etc. QA274.75D54 1991 519.2 90-47081 ISBN 978-1-4612-6739-3 ISBN 978-1-4612-0389-6 (eBook) CIP DOI 10.1007/978-1-4612-0389-6 Printed on acid -free paper.
e Springer Science+Business Media New York 1992. Originally published by Birkhlluser Boston in 1992. Copyright is not claimed for works of U.S. Govemrnent employees. An rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permis sion of the copyright owner. Permission 10 photocopy for intemal or personal use, or the intema! or personal use of specific clients, is granted by Birkhăuser Boston for libraries and otherusers registered with the Copyright Clearance Center (CCC), provided that the base fee of $0.00 per copy, plus $.20 per page is paid directly 10 CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed directly to Springer Science+Business Media, LLC. ISBN 978-1-4612-6739-3 Camera-ready text prepared by the Authors.
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CONTENTS Preface Conference Participants Part I : Diffusion Processes and General Stochastic Flows on Manifolds Stability and equilibrium properties of stochastic flows of diffeomorphisms P. BAXENDALE . . . . . . . . . . . . . . . . . . . . . . 3 Stochastic flows on Riemannian manifolds K.D. ELWORTHY . . . . . . . . . . . . . . . . . . . . 37
Part II: Special Flows and Multipoint Motions Isotropic stochastic flows R.W.R. DARLING . . .
. . . 75
The existence of isometric stochastic flows for Riemannian Brownian motions M. LIAO . . . . . . . . . . . . . . . . . . . . .
95
Time-reversal of solutions of equations driven by Levy processes P. SUNDAR . . . . . . . . . . . . . . . . . . . . . . . 111 Birth and death on a flow E. GINLAR and J .S. KAO
. . . . . . . . . . . . . . . . 121
Part III: Infinite Dimensional Systems Lyapunov exponents and stochastic flows of linear and affine hereditary systems S.E.A. MOHAMMED . . . . . . . .
