Stochastic Analysis and Related Topics VI: Proceedings of the Sixth Oslo—Silivri Workshop Geilo 1996 PDF
Preview Stochastic Analysis and Related Topics VI: Proceedings of the Sixth Oslo—Silivri Workshop Geilo 1996
Progress in Probability Volume 42 Series Editors Thomas Liggett Charles Newman Loren Pitt Stochastic Analysis and Related Topics VI Proceedings of the Sixth Oslo-Silivri Workshop Geilo 1996 L. Decreusefond Jon Gjerde B. 0ksendal A.S. Üstünel Editors Springer Science+Business Media, LLC Laurent Decreusefond Jon Gjerde Ecole Nationale Superieure Central Bureau of Statistics des Telecommunications Norwegian Computing C enter Departement Reseaux N-0316 Oslo, Norway 75634 Paris Cedex, France Ali Süleyman Üstünel Bernt 0ksendal Ecole Nationale Superieure University of Oslo des Telecommunications Department of Mathematics Departement Reseaux N-0316 Oslo, Norway 75634 Paris Cedex, France Library of Congress Cataloging-in-Publication Data Stochastic analysis and related topics VI : the Geilo workshop, 1996 / Laurent Decreusefond ... [et a.], editors. p. cm. ~ (Progress in probability ; v. 42) Papers from the Sixth Oslo-Silivri Workshop on Stochastic Analysis held in Geilo from July 29-Aug. 6,1996. ISBN 978-1-4612-7385-1 ISBN 978-1-4612-2022-0 (eBook) DOI 10.1007/978-1-4612-2022-0 1. Stochastic analysis-Congresses. I. Decreusefond, Laurent, 1966- . II. Oslo-Silivri Workshop on Stochastic Analysis (6th : 1996 : Geilo, Norway) III. Series: Progress in probability ; 42. QA274.2.S77163 1977 519.2-dc21 97-29125 AMS Subject Classifications: 60R 60H07. 60H15. 60H3Q Printed on acid-free paper © 1998 Springer Science+Business Media New York Originally published by Birkhäuser Boston in 1998 Softcover reprint of the hardcover 1st edition 1998 Copyright is not claimed for works of U.S. Government employees. 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, photocopy ing, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Springer Science+Business Media, LLC for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 222 Rosewood Drive, Danvers, MA 01923, U.S.A. Special requests should be addressed directly to Springer Science+Business Media, LLC ISBN 978-1-4612-7385-1 Reformatted from authors' disks in Latex by TEXniques, Inc., Boston, MA. Printed and bound by Quinn-Woodbine, Woodbine, N.J. 9 8 7 6 5 4 3 21 Contents Main Lectures 1 Stochastic Differential Systems With Memory. Theory, Examples and Applications. S.-E. A. Mohammed 1 2 Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order E. Pardoux 79 Contributed Papers 3 Stochastic Analysis on Lie Groups A.S. Ustiinel 129 4 A Conditional Independence Property for the Solution of a Linear Stochastic Differential Equation with Lateral Conditions A. Alabert and M. Ferrante 159 5 Numerical Solution of the Pressure Equation for Fluid Flow in a Stochastic Medium F.E. Benth and J. Gjerde 175 6 The Burgers Equation with a Non-Gaussian Random Force F.E. Benth and L. Streit 187 7 A Verification Theorem for Combined Stochastic Control and Impulse Control K.A. Brekke and B. 0ksendal 211 8 Energy Identities and Estimates for Anticipative Stochastic Integrals on a Riemannian Manifold A.B. Cruzeiro and P. Malliavin 221 9 On Conditional Characteristic Functions of Second Order Wiener Functionals L. Decreusefond and A.S. Ustiinel 235 VI Contents 10 A Variation of Parameters Solution of a Quasilinear Skohorod SDE using the Wick Product H. K. Gjessing 245 11 Diagonal Estimates of Transition Densities for Jump Processes in Small Time Y. Ishikawa and R. Leandre 251 12 Non-Kolmogorov Probabilistic Models with p-adic Probabilities and Foundations of Quantum Mechanics A. Khrennikov 275 13 Smoothness of the Solution Operator of Stochastic Differential Equations with Infinite Dimensional Parameters T.S. Knudsen 305 14 Nonlinear SPDEs: Colombeau Solutions and Pathwise Limits M. Oberguggenberger and F. Russo 319 15 Construction of a Quantum Field Linked to the Coulomb Potential N. Privault 333 16 The Sard Inequality on Two Non-Gaussian Spaces N. Privault 349 17 Regularity of the Law for a Class of Anticipating Stochastic Differential Equations C. Rovira and M. Sanz-Sole 357 18 Fubini's Theorem for Plane Stochastic Integrals J. Salazar 373 19 Stability and Vanishing Viscosity for a Class of SPDEs Related to Turbulent Transport G. Vage 379 20 Probabilistic Interpretation of the Symmetry Group of Heat Equations J. C. Zambrini 387 21 On the Strong Feller Property of the Semi-Groups Generated by Non-Divergence Operators with LP Drift M. Rockner and T.S. Zhang 401 Foreword This volume contains the contributions of the participants of the Sixth Oslo-Silivri Workshop on Stochastic Analysis, held in Geilo from July 29 to August 6, 1996. There are two main lectures • Stochastic Differential Equations with Memory, by S.E. A. Mohammed, • Backward SDE's and Viscosity Solutions of Second Order Semilinear PDE's, by E. Pardoux. The main lectures are presented at the beginning of the volume. There is also a review paper at the third place about the stochastic calculus of variations on Lie groups. The contributing papers vary from SPDEs to Non-Kolmogorov type probabilistic models. We would like to thank • VISTA, a research cooperation between Norwegian Academy of Sciences and Letters and Den Norske Stats Oljeselskap (Statoil), • CNRS, Centre National de la Recherche Scientifique, • The Department of Mathematics of the University of Oslo, • The Ecole Nationale Superieure des Telecommunications, for their financial support. L. Decreusefond J. Gjerde B. 0ksendal A.S. Ustunel PARTICIPANTS TO THE 6TH WORKSHOP ON STOCHASTIC ANALYSIS Vestlia H¢yfjellshotell, Geilo, Norway, July 28 - August 4, 1996. Aureli ALABERT E-mail: [email protected] Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: [email protected] 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: [email protected] Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I. NORWAY Universite de Provence E-mail: [email protected] 39, rue Joliot Curie Vlad BALLY 13453 MARSEILLE Cedex 13 Departement de probabilites FRANCE Universite Paris VI E-mail: [email protected] 4, place Jussieu Marco FERRANTE 75252 Paris cedex 05 Department of Mathematics FRANCE E-mail: [email protected] University of Padova Fred Espen BENTH Via Belzoni Norwegian Computing Centre 7-35100.Padova Box 114 Blindern ITALY N-0314 Oslo E-mail: [email protected] NORWAY Nils Chr. FRAMSTAD E-mail: [email protected] Dept. of Mathematics Kjell BLEIVIK University of Oslo Hofstadgaten 44 Box 1053 Blindern N-1370 Asker N-0316 Oslo NORWAY NORWAY E-mail E-mail: [email protected] Ana Bela CRUZEIRO Jon GJERDE Grupo de Fisica-Matematica Central Bureau of Statistics Av. Prof. Gama Pinto 2 Box 8131 DEP 1699 Lisboa codex N-0033 Oslo PORTUGAL NORWAY E-mail: [email protected] DK-2800 Lyngby DENMARK Hakon GJESSING E-mail: [email protected] Section for Medical Informatics & Statistics Eddy MAYER-WOLF AHH, Haukeland Hospital Dept. of Mathematics N-5021 Bergen, NORWAY Technion E-mail: [email protected] Haifa 32000 ISRAEL Axel GRORUD E-mail:[email protected] C.M.I. Salah MOHAMMED Universite de Provence Dept. of Mathematics 39, rue Joliot Curie Southern Illinois University 13453 MARSEILLE Cedex 13 Carbondale FRANCE Illinois 62901-4408 E-mail:[email protected]·fr U.S.A. Christian HEGGEN E-mail: [email protected] Dept. of Mathematics Trond MYHRE University of Oslo Dept. of Mathematics Box 1053 Blindern University of Oslo N-0316 Oslo Box 1053 Blindern NORWAY N-0316 Oslo E-mail: [email protected] NORWAY Yasushi ISHIKAWA E-mail: [email protected] Institute of Mathematics University of Tsukuba MichaelOBERGUGGENBERGER Tsukuba, 305 Institut fuer Mathematik und Geometrie JAPAN Universitaet Innsbruck E-mail: [email protected] Technikerstrasse 13 A - 6020 Innsbruck Espen R. JACOBSEN AUSTRIA Astrid Aasensv. 2 E-mail: [email protected] 7017 Trondheim NORWAY Bernt OKSENDAL Email: [email protected] Dept. of Mathematics Andrei KHRENNIKOV University of Oslo Mathematical Institute Box 1053 Blindern Bochum University, D-44780 N-0316 Oslo GERMANY NORWAY Email: [email protected] E-mail:[email protected] Thomas Skov KNUDSEN Etienne PARDOUX Department of Mathematics Mathematiques, URA 225 Technical University of Denmark Universite de Provence Building 303 13331 Marseille Cedex 3 FRANCE Paul A. TORVUND E-mail: [email protected] Dept. of Mathematics University of Oslo Nicolas PRIVAULT Box 1053 Blindern Equipe d' Analyse et Probabili tes N-0316 Oslo Universite d'Evry NORWAY Boulevard des Coquibus E-mail: [email protected] 91025 Evry Cedex FRANCE Jan UBOE E-mail: [email protected] Stord/Haugesund College Kristin REIKVAM Skaaregaten 103 Dept. of Mathematics 5500 Haugesund University of Oslo NORWAY Box 1053 Blindern E-mail: [email protected] N-0316 Oslo Ali Siileyman USTUNEL NORWAY Ecole Nationale Superieure des Telecom E-mail: [email protected] munications Jorge SALAZAR Departement Reseaux CMAF-COMPLEXO II 46, rue Barrault Av. Gama Pinto N r2 75634 Paris Cedex 13 1699 Lisbon Codex FRANCE PORTUGAL E-mail: [email protected] E-mail: [email protected] Henning VARNER Stig SANDNES Dept. of Mathematics Dept. of Mathematics University of Oslo University of Oslo Box 1053 Blindern Box 1053 Blindern N-0316 Oslo N-0316 Oslo NORWAY NORWAY E-mail: [email protected] E-mail: [email protected] Marta SANZ-SOLE Gjermund VAGE Facultat de Matematiques Dept. of Mathematics Universitat de Barcelona University of Oslo Gran Via, 585 Box 1053 Blindern 08007 Barcelona N-0316 Oslo SPAIN E-mail:[email protected] NORWAY E-mail: [email protected] Rune TOKLE Dept. of Mathematics Jean-Claude ZAMBRINI University of Oslo Group of Mathematical Physics Box 1053 Blindern Av. Prof. Gama Pinto 2 N-0316 Oslo 1699 Lisboa codex NORWAY PORTUGAL E-mail: [email protected] E-mail: [email protected]
The list of books you might like
