Progress in Probability

Transcription

1 Progress in Probability Volume 26 Series Editors Thomas Liggett Charles Newman Loren Pitt

2 Stochastic Analysis and Applications Proceeding S of the 1989 Lisbon Conference A.B. Cruzeiro I.C. Zambrini Editors Springer Science+Business Medi~ LLC

3 Ana Bela Cruzeiro Instituto de Fisica e Matematica (INIC) 1699 Lisboa Codex, Portugal Iean Claude Zambrini Department of Mathematics Royal Institute of Technology S-I0044 Stockholm, Sweden Library of Congress Cataloging-in-Publication:Data Stochastic analysis and applications : proceedings of the 1989 Lisbon conference I A.B. Cruzeiro, I.C. Zambrini, editors. p. cm. -- (Progress in probability : v.26) Papers from the First Lisbon Conference on Stochastic Analysis and Applications, held Sept Includes bibliographical references. ISBN ISBN (ebook) DOI / (hard : acid-free) 1. Stochastic analysis -- Congresses. I. Cruzeiro, A.B. (Ana Bela Ferreira), Zambrini, Iean-Ciaude. III. Lisbon Conference on Stochastic Analysis and Applications (1st: 1989) IV. Series: Progress in probability : 26. QA274.2.S dc20 Printed on acid-free paper CIP Springer Science+Business Media New York 1991 Origina11y published by Birkhäuser Boston in 1991 Softcover reprint ofthe hardcover 1st edition 1991 All 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 permission of the copyright owner. Permission to photocopy for internal or personal use, or by the internal or personal use of specific clients, is granted by Birkhäuser Boston for libraries and others users registered with the Copyright Clearance Center (CCC), provided that the base fee of $0.00 per copy, plus $0.20 per page is paiddirectly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed direct1y to Springer Science+ Business Media, LLC. ISBN Typeset by Authors in TeX and AMS TeX

4 Contents Preface.. Contributors Conform ally Invariant Random Fields and Processes - Old and New S. Albeverio, K. Iwata, T. Kolsrud.... vii. viii 1 Diffusion Processes with Singular Dirichlet Forms Sergio Albeverio, Zhi Ming Ma Geometric Quantization on Wiener Manifolds Lars Andersson, Gunnar Peters Heat Kernels on Lie Groups Maria Teresa Arede Weak Sobolev Inequalities Dominique Bakry Feynman's Functional Calculus and Stochastic Calculus of Variations Ana Bela Cruzeiro and Jean Claude Zambrini Manifolds and Graphs with Mostly Positive Curvatures K.D. Elworthy The Thorn Class of Mathai and Quillen and Probability Theory Ezra Getzler The General Mathematical Framework of Euclidean Quantum Mechanics: An Outline Torbjom Kolsrud and Jean Claude Zambrini

5 vi Contents Naturality of Quasi-Invariance of Some Measures Paul Malliavin Stochastic Differential Equations with Boundary Conditions David Nualart and Etienne Pardoux Sobolev Inequalities and Polynomial Decay of Convolution Powers and Random Walks Laurent SalofJ-Coste Microcanonical Distributions for One Dimensional Lattice Gases Daniel W. Stroock

6 Preface At the end of the summer 1989, an international conference on stochastic analysis and related topics was held for the first time in Lisbon (Portugal). This meeting was made possible with the help of INIC and JNICT, two organizations devoted to the encouragement of scientific research in Portugal. The meeting was interdiciplinary since mathematicians and mathematical physicists from around the world were invited to present their recent works involving probability theory, analysis, geometry and physics, a wide area of cross fertilization in recent years. Portuguese scientific research is expanding fast, these days, faster, sometimes, than the relevant academic structures. The years to come will be determinant for the orientation of those young Portuguese willing to take an active part in the international scientific community. Lisbon's summer 89 meeting should initiate a new Iberic tradition, attractive both for these researchers to be and, of course, for the selected guests. Judging by the quality of contributions collected here, it is not unrealistic to believe that a tradition of "southern randomness" may well be established. vii

7 Contributors S. Albeverio, Fakultat fur Mathematik, Ruhr Universitat, D-4630 Bochum, Germany and BiBos Research Center, Universitat Bielefeld, Bielefeld, Germany, and SFB 237-Essen, Bochum, Diisseldorf; CERFIM, Locarno, Switzerland Lars Andersson, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden Maria Teresa Arede, Faculdade de Engenharia-DEMEC, R. dos Bragas, P-4000 Porto, Portugal Dominique Bakry, Laboratoire de Statistique et Probabilites, Universite Paul Sabatier, 11B, route de Narbonne, 31062, Toulouse Cedex, France Ana Bela Cruzeiro, Instituto de Fisica e Matematica (INIC), Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal K. D. Elworthy, Mathematics Institute, University of Warwick, Coventry CV 4 7 AL, England Ezra Getzler, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA K. Iwata, Fakultat fur Mathematik, Ruhr Universitat, D-4630 Bochum, Germany, and SFB-237, Bochum-Essen-Diisseldorf, Germany T. K olsrud, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden Zhi Ming Ma, BiBos Research Center, D-4BOO Bielefeld, Germany, on leave of absence from the Institute of Applied Mathematics, Academia Sinica, Beijing, People's Republic of China Paul Malliavin, 10 rue Saint-Louis en l'ile, Paris, France David Nualart, Facultat de Matematiques, Universitat de Barcelona, Gran Via, OB007 Barcelona, Spain Etienne Pardoux, MathCmatiques, URA 225, Universite de Provence, 1331 Marseille Cedex 3, France Gunnar Peters, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden Laurent SalofJ-Coste, Universite de Paris VI-CNRS, Analyse Complexe et Geometrie (URA D213), 4, place Jussieu - Tour , Paris Cedex 05, France Daniel W. Stroock, Massachusetts Institute of Technology, Room 2-272, Cambridge, MA 02139, USA Jean Claude Zambrini, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, and Instituto de Fisica e Matematica (INIC), Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal viii