thematical Analysis of Mathematical Analysis of Random Phenomena Downloaded from Tandom Phenomena

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1 Mathematical Analysis of Random Phenomena Downloaded from thematical Analysis of Tandom Phenomena Proceedings of the International Conference

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3 Mathematical Analysis of Random Mathematical Analysis of Random Phenomena Downloaded from Phenomena 0 Hammamet, Tunisia September 2085 Editors Ana Bela Cruzeiro Brupo de Fisica-Matemiitica &. Universidade Tknica de bisboa, Portugal Habib Ouerdiane University of Tunis El Manar, Tunisia Nobuaki Obata Tohoku University, Japan NEW JERSEY LONDON * SINGAPORE * BElJlNG * SHANGHAI * HONG KOMG * TAIPEI - CHEMNAI

4 Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore USA ofice: 27 Warren Street, Suite , Hackensack, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Mathematical Analysis of Random Phenomena Downloaded from British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. MATHEMATICAL ANALYSIS OF RANDOM PHENOMENA Proceedings of the International Conference Copyright by World Scientific Publishing Co. Re. Ltd. All rights reserved. This book, or parts tliereoj may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any inforniation 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-I ISBN Printed in Singapore by World scientific Printers (S) Pte Ltd

5 Preface Mathematical Analysis of Random Phenomena Downloaded from This volume contains research articles resulting of the International Conference on Mathematical Analysis of Random Phenomena that took place in Hammamet, Tunisia, from 12 to 17 September 2005 and was Coorganized by the Portuguese Mathematical Society (SPM) and the Tunisian Mathematical Society (SMT). This meeting was devoted to the exposition of recent developments in the mathematical analysis of random phenomena: stochastic analysis and its applications, mathematical physics, infinite dimensional analysis, probability theory and their interactions. One can read in this volume eighteen articles on the following topics: stochastic analysis and infinite dimensional analysis, white noise analysis, Malliavin calculus and applications, mathematical finance, Poisson analysis, hydrodynamics, statistical mechanics, and probability in quantum physics. We are grateful to all Tunisian and Portuguese institutions which have brought to the scientific organizing committee their moral and financial supports. These are, in particular,. Ministhre Tunisien de 1 Enseignement Suphrieur,. Ministbe de la Recherche Scientifique, de la Technologie et du Dhveloppement des Comphtences, Tunisia GRICES,. UniversitQ de Tunis El Manar,. University of Lisbon, Grupo de Fisica MatemLtica,. University of Madeira, Centro de Cihcias Matemgticas,. Socihth Mathhmatique de Tunisie,. Sociedade Portuguesa de MatemLtica,. Faculth des Sciences de Tunis. We wish also to thank the authors for their contribution to a book of high quality, accessible to a large scientific public, as well as the colleagues who helped us with their anonymous and careful referee work. The Editors, ANA BELA CRUZEIRO, NOBUAKI OBATA, HABIB OUERDIANE Lisbon / Sendai / Tunis, July 12, 2006 V

6 Mathematical Analysis of Random Phenomena Downloaded from Contents Preface HBLENE AIRAULT Geometry and integration by parts on H \ Diff(S') HBLENE AIRAULT, PAUL MALLIAVIN Invariant measures for Ornstein-Uhlenbeck operators ABDULRAHMAN AL-HUSSEIN Backward stochastic differential equations with respect to martingales WIDED AYED, NOBUAKI OBATA, HABIB OUERDIANE Partial unitarity arising from quadratic quantum white noise SONIA CHAARI, SOUMAYA GHERYANI, HABIB OUERDIANE Schilder's theorem for Gaussian white noise distributions F. CIPRIANO, H. OUERDIANE, J. L. SILVA, R. VILELA MENDES A nonlinear stochastic equation of convolution type FERNANDA CIPRIANO, ANA BELA CRUZEIRO Variational principle for diffusions on the diffeomorphism group with the H2 metric DIOGO AGUIAR GOMES On a variational principle for the Navier-Stokes equation HANNO GOTTSCHALK, HABIB OUERDIANE, BOUBAKER SMII Convolution calculus on white noise spaces and Feynman graph representation of generalized renormalization flows TAKEYUKI HIDA, SI SI Characterizations of standard noises and applications YUH-JIA LEE, HSIN-HUNG SHIH Analysis of stable white noise functionals PAUL LESCOT Unitarizing measures for a representation of the Virasoro algebra, according to Kirillov and Malliavin: state of the problem YUTAO MA, NICOLAS PRIVAULT FKG inequality on the Wiener space via predictable representation R. VILELA MENDES Path-integral estimates of ground-state functionals GIULIA DI NUNNO, BERNT DKSENDAL A representation theorem and a sensitivity result for functionals of jump diffusions WILHELM VON WALDENFELS Creation and annihilation operators on locally compact spaces JEAN-CLAUDE ZAMBRINI From the geometry of parabolic PDE to the geometry of SDE List of participants V vii