An existence result for infinite-dimensional Brownian diffusions with non-regular and non-Markovian drift
- Dai Pra, Paolo
- Rœlly, Sylvie
2010 Mathematics Subject Classification
- 60G15 60G60 60H10 60J60
- infinite-dimensional Brownian diffusion, space-time Gibbs field, cluster expansion
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 · ∞ 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.