Short-time Gibbsianness for infinite-dimensional diffusions with space-time interaction

  • We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finiterange uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t0 > 0 such that the distribution at time t = t0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.

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Author:Frank Redig, Sylvie Roelly, Wioletta Ruszel
Series (Serial Number):Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2009, 04)
Document Type:Preprint
Year of Completion:2009
Publishing Institution:Universität Potsdam
Release Date:2011/03/31
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht