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STOCHASTIC PROCESSES IN ANALYSIS

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.

Funding Scheme

CSC - Cost-sharing contracts

Coordinator

University of Edinburgh
Address
Old College South Bridge
EH1 1HN Edinburgh
United Kingdom

Participants (5)

RUHR-UNIVERSITY BOCHUM
Germany
Address
Universitaetsstrasse 150
44780 Bochum
UNIVERSITE DE PARIS-SUD XI
France
Address
Rue Georges Clemenceau 15
91405 Orsay
UNIVERSITE PIERRE ET MARIE CURIE - PARIS VI
France
Address
Place Jussieu 4
75252 Paris
UNIVERSITY OF BIELEFELD
Germany
Address
Universitätsstraße 25
33501 Bielefeld
University of Warwick
United Kingdom
Address
Gibbet Hill Road
CV4 7AL Coventry