Abstract
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.
Original language | English |
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Pages (from-to) | 653-674 |
Number of pages | 22 |
Journal | Markov Processes and Related Fields |
Volume | 20 |
Issue number | 4 |
Publication status | Published - 2014 |
Keywords
- infinite-dimensional diffusion
- cluster expansion
- non-Markov drift
- Girsanov formula
- ultracontractivity
- planar rotors