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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| 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 |
| Publication 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): |  Keine öffentliche Lizenz: Unter Urheberrechtsschutz |
| External remark: | MSC - Klassifikation: 60K35 , 60H10 |
