An Existence Result for Infinite-Dimensional Brownian Diffusions with Non-Regular and Non-Markovian Drift

#### P. Dai Pra, S. Roelly

2004, v.10, Issue 1, 113-136

ABSTRACT

We prove in this paper an existence result for infinite-dimensional
stationary interactive Brownian diffusions. The interaction is
supposed to be small in the norm $\|\cdot\|_{\infty}$ but otherwise
is very general, being possibly non-regular and non-Markovian.
Our method consists in using the characterization of such diffusions
as space-time Gibbs fields so that we construct them by
space-time cluster expansions in the small coupling parameter.

Keywords: infinite-dimensional Brownian diffusion, space-time Gibbs field, cluster expansion