Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction

  • We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.

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Metadaten
Author details:Sylvie RoellyGND, Wioletta M. Ruszel
URN:urn:nbn:de:kobv:517-opus-69014
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (2(2013)18)
Publication type:Preprint
Language:English
Completion year:2013
Publishing institution:Universität Potsdam
Release date:2013/12/16
Tag:Girsanov formula; cluster expansion; infinite-dimensional diffusion; non-Markov drift; ultracontractivity
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
License (German):License LogoUrheberrechtsschutz
External remark:MSC - Klassifikation: 60K35 , 60H10