Stochastic Analysis Proceedings of the Japanese-French Seminar held
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1322 M. Metivier S. Watanabe (Eds.)
Stochastic Analysis Proceedings of the Japanese-French Seminar held in Paris, France, June 16-19, 1987
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Michel Metivier Departernent de Mathematiques Appliquees Ecole Polytechnique 91128 Palaiseau, France Shinzo Watanabe Department of Mathematics, Faculty of Science Kyoto University, Kyoto, 606 Japan
Mathematics Subject Classification (1980): 60F, 60G, 60H, 60J ISBN 3-540-19352-9 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-19352-9 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
PREFACE
As a project under the France-Japan Cooperative Science Program sponsored by C.N.R.S. (Centre National de la Recherche Scientifique) and J.S.P.S. (Japan Society for the Promotion of Science), a joint seminar on probability theory was held June 16-19, 1987, at Ecole Normale Superieure, Paris. The main theme was stochastic analysis and applications to large scale systems. Nineteen lectures were presented on various topics like the Malliavin calculus, infinite dimensional stochastic differential equations and stochastic partial differential equations, limit theorems for particle systems, diffusions in random environment, hydrodynamical models, etc. This volume of the Springer Lecture Notes is devoted to the original papers presented by the participants. A few lectures given at the seminar correspond to papers already published or being published elsewhere and are therefore absent from this volume. Because of the variety of the problems studied in those lectures, we did not find proper to try to group them -rather artificially- by topics, and adopted the alphabetic order of authors. We would express our sincere thanks to contributors of this volume, all the participants of the seminar and also to Professor T. Hida who could not participate but, without whose kind advice and suggestions, this seminar could not have been realized. It is also our pleasure to give our appreciation to Springer-Verlag for the prompt and efficient publication of the volume and Mrs Jeanne Bailleul for her help in the organization of the meeting and the preparation of the final volume.
February 5, 1988 Michel METIVIER - Shinzo WATANABE
TABLE OF CONTENTS G. BENAROUS Noyau de la chaleur hypoelliptique et geometrie sous-riemannienne M. FUKUSHIMA On t
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