Objective The project has coordinated work in Europe in key areas including stochastic differential geometry, stochastic partial differential equations, Malliavin calculus, harmonic analysis and the properties of Brownian Motion. Meetings were organized in Warwick and Paris, and many insits by international experts to individual institutes were arranged.The project employed a computing officer, who developed practical second order algorithms for numerically integrated strong solutions to stochastic differential equations. These have been successfully implemented. Work also proceeded on the numerical integration of stochastic partial differential equations.The coordination of effort will be directed to the following goals. 1. Study of analysis in infinite dimensions especially Dirichlet processes and their geometry (e.g. the Ornstein-Uhlenbeck process and those connected with Quantum Fields). In particular, study of the associated potential theory, Martin boundary and random fields. The study of gauge fields and string models. The study of stochastic differential geometric structures in connection with index theory, on loop spaces for example. 2. Study of Dirichlet forms in finite dimensional spaces. In particular we mention the relation with singular Schroedinger operators, the study of hypoelliptic differential operators and associated processes, he asymptotics of the heat kernel on manifolds and Lie groups. The study of the stochastic calculus associated with Dirichlet spaces. 3. Study of detailed properties of Brownian motion, e.g. self-avoiding random walks, polymer models and quantum fields. Behaviour of Brownian motion on manifolds in relation with geometric properties, for example the Martin boundary. Fields of science natural scienceschemical sciencespolymer sciencesnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP2-SCIENCE - Programme plan (EEC) to stimulate the international cooperation and interchange needed by European research scientists (SCIENCE), 1988-1992 Topic(s) Data not available Call for proposal Data not available Funding Scheme CSC - Cost-sharing contracts Coordinator University of Edinburgh EU contribution No data Address Old College South Bridge EH1 1HN Edinburgh United Kingdom See on map Total cost No data Participants (5) Sort alphabetically Sort by EU Contribution Expand all Collapse all RUHR-UNIVERSITY BOCHUM Germany EU contribution No data Address Universitaetsstrasse 150 44780 BOCHUM See on map Total cost No data UNIVERSITE DE PARIS-SUD XI France EU contribution No data Address RUE GEORGES CLEMENCEAU 15 91405 ORSAY See on map Total cost No data UNIVERSITE PIERRE ET MARIE CURIE - PARIS VI France EU contribution No data Address Place Jussieu 4 75252 PARIS See on map Total cost No data UNIVERSITY OF BIELEFELD Germany EU contribution No data Address Universitätsstraße 25 33501 BIELEFELD See on map Total cost No data University of Warwick United Kingdom EU contribution No data Address Gibbet Hill Road CV4 7AL Coventry See on map Total cost No data