An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift

  • 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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Author:Sylvie Roelly, Paolo Dai Pra
Document Type:Postprint
Year of Completion:2004
Publishing Institution:Universität Potsdam
Release Date:2006/03/17
Tag:cluster expansion; infinite-dimensional Brownian diffusion; space-time Gibbs field
Source:Markov Processes and Related Fields. - 10 (2004), S. 113 - 136
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Collections:Universität Potsdam / Aufsätze (Pre- und Postprints) / Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik / Wahrscheinlichkeitstheorie
Notes extern:
AMS Classifications: 60G15 , 60G60 , 60H10 , 60J60