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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. Körezlioglu, B. 0ksendal, A. S. Üstünel MATHEMATICAL THEORY OF COMMUNICATION NETWORKS VENKAT ANANTHARAM EECS DEPARTMENT UNIVERSITY OF CALIFORNIA BERKELEY, CA 94720 ananth@vyasa.eecs.berkeley.edu Abstract We describe so me recent advances in the mathematical theory of com munication networks.
List of contents
Main Lectures.- Mathematical Theory of Communication Networks.- State-Space Models of the Term Structure of Interest Rates.- Theory of Capacity on the Wiener Space.- Contributed Papers.- A Model for Loss of Profits Insurance.- A Note on Population Growth in a Crowded Stochastic Environment.- A Generalized Feynman-Kac Formula for the Stochastic Heat Problem with Anticipating Initial Conditions.- Wick products of Complex Valued Random Variables.- Two Classes of Stochastic Dirichlet Equations which Admit Explicit Solution Formulas.- Semi-Implicit Euler-Maruyama Scheme for Stiff Stochastic Equations.- Wick Approximation of Quasilinear Stochastic Differential Equations.- The Circle as a Fermionic Distribution.- Linear Skorohod Stochastic Differential Equations on Poisson Space.- Diffusion Approximation for Elliptic Stochastic Differential Equations.- Absolute Continuity of Monotone Shifts on the Wiener Space.- Hilbert Space Methods Applied to Elliptic Stochastic Partial Differential Equations.
