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.
| Identifer | oai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:6901 |
| Date | January 2013 |
| Creators | Roelly, Sylvie, Ruszel, Wioletta M. |
| Publisher | Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik |
| Source Sets | Potsdam University |
| Language | English |
| Detected Language | English |
| Type | Preprint |
| Format | application/pdf |
| Rights | http://opus.kobv.de/ubp/doku/urheberrecht.php |
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