We prove in this paper an existence result for in nite-dimensional stationary weakly interactive Brownian diusions. The interaction is very general in the sense that it is not supposed to be regular, and it also could be non-Markovian, but it is small enough. Our method consists in using the characterization of such diusions as space-time Gibbs elds so that we construct them by space-time cluster expansions in the small coupling parameter.
An existence result for infinite-dimensional Brownian diffusions with non-regular and non-Markovian drift
DAI PRA P.;
2004-01-01
Abstract
We prove in this paper an existence result for in nite-dimensional stationary weakly interactive Brownian diusions. The interaction is very general in the sense that it is not supposed to be regular, and it also could be non-Markovian, but it is small enough. Our method consists in using the characterization of such diusions as space-time Gibbs elds so that we construct them by space-time cluster expansions in the small coupling parameter.
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