WIAS Preprint No. 717, (2002)

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.

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