Bernt Oksendal - Böcker

This book is a result of recent developments in several fields. Mathematicians, statisticians, finance theorists, and economists found several interconnections in their research. The emphasis was on common methods, although the applications were also interrelated. The main topic is dynamic stochastic models, in which information arrives and decisions are made sequentially. This gives rise to what finance theorists call option value, what some economists label quasi-option value. Some papers extend the mathematical theory, some deal with new methods of economic analysis, while some present important applications, to natural resources in particular.

The main emphasis of this work is on stochastic partial differential equations. First the stochastic Poisson equation and the stochastic transport equation are discussed; then the authors go on to deal with the Schrodinger equation, the heat equation, the nonlinear Burgers' equation with a stochastic source, and the pressure equation. The white noise approach often allows for solutions given by explicit formulas in terms of expectations of certain auxiliary processes. The noise in the above examples are all of a Gaussian white noise type. In the end, the authors also show how to adapt the analysis to SPDEs involving noise of Poissonian type.

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. E-mail: abc@gfm.cii.fc.ui.pt Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom- 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: alabert@mat.uab.es 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: decreuse@res.enst.fr Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I.

One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro­ cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas­ tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log­ Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the­ art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.

One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro­ cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas­ tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log­ Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the­ art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.

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. E-mail: abc@gfm.cii.fc.ui.pt Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom- 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: alabert@mat.uab.es 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: decreuse@res.enst.fr Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I.