Over the last years, stochastic analysis has had an enormous progress with the impetus originating from different branches of mathematics: PDE's and the Malliavin calculus, quantum physics, path space analysis on curved manifolds via probabilistic methods, and more.

This volume contains selected contributions which were presented at the 8th Silivri Workshop on Stochastic Analysis and Related Topics, held in September 2000 in Gazimagusa, North Cyprus.

The topics include stochastic control theory, generalized functions in a nonlinear setting, tangent spaces of manifold-valued paths with quasi-invariant measures, and applications in game theory, theoretical biology and theoretical physics.

Contributors: A.E. Bashirov, A. Bensoussan and J. Frehse, U. Capar and H. Aktuglul, A.B. Cruzeiro and Kai-Nan Xiang, E. Hausenblas, Y. Ishikawa, N. Mahmudov, P. Malliavin and U. Taneri, N. Privault, A.S. Ustunel"

This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. "Infinitely divisible random measures and superprocesses" by D.A. Dawson, 2. "Dirichlet forms on infinite dimensional spaces and appli- cations" by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ- ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini- tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A. S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESSES DONALD A. DAWSON 1. Introduction.

Over the last years, stochastic analysis has had an enormous progress with the impetus originating from different branches of mathematics: PDE's and the Malliavin calculus, quantum physics, path space analysis on curved manifolds via probabilistic methods, and more.

This volume contains selected contributions which were presented at the 8th Silivri Workshop on Stochastic Analysis and Related Topics, held in September 2000 in Gazimagusa, North Cyprus.

The topics include stochastic control theory, generalized functions in a nonlinear setting, tangent spaces of manifold-valued paths with quasi-invariant measures, and applications in game theory, theoretical biology and theoretical physics.

Contributors: A.E. Bashirov, A. Bensoussan and J. Frehse, U. Capar and H. Aktuglul, A.B. Cruzeiro and Kai-Nan Xiang, E. Hausenblas, Y. Ishikawa, N. Mahmudov, P. Malliavin and U. Taneri, N. Privault, A.S. Ustunel"

This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. "Infinitely divisible random measures and superprocesses" by D.A. Dawson, 2. "Dirichlet forms on infinite dimensional spaces and appli- cations" by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ- ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini- tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A. S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESSES DONALD A. DAWSON 1. Introduction.

This volume contains the contributions of the participants to the Oslo- Silivri Workshop on Stochastic Analysis, held in Silivri, from July 18 to July 29, at the Nazlm Terzioglu Graduate Research Center of Istanbul University. 1994, There were three lectures: * Mathematical Theory 0/ Communication Networks by V. Anantharam, * State-Space Models 0/ the Term Structure o/Interest Rates, by D. Duffie, * Theory 0/ Capacity on the Wiener Space, by F. Hirsch. The main lectures are presented at the beginning of the volume. The contributing papers cover different domains varying from random fields to dis- tributions on infinite dimensional spaces. We would like to thank the following organizations for their financial sup- port: * VISTA, a research cooperation between the Norwegian Academy of Scineces and Letters and Den Norske Stats Oljeselskap A. S. (Statsoil). * Ecole Nationale Superieure des Telecommunications de Paris. In the summer of 1994 we lost our dear friend and colleague ALBERT BADRIKIAN. We are dedicating this volume to his memory. H. Korezlioglu, B. 0ksendal, A. S. Ustunel MATHEMATICAL THEORY OF COMMUNICATION NETWORKS VENKAT ANANTHARAM * EECS DEPARTMENT UNIVERSITY OF CALIFORNIA BERKELEY, CA 94720 [email protected] Abstract We describe so me recent advances in the mathematical theory of com- munication networks.