@article{RoellyRuszel2014,
  author    = {Roelly, Sylvie and Ruszel, W. M.},
  title     = {Propagation of gibbsianness for infinite-dimensional diffusions with space-time interaction},
  series = {Markov processes and related fields},
  volume    = {20},
  journal   = {Markov processes and related fields},
  number    = {4},
  publisher = {Polymat},
  address   = {Moscow},
  issn      = {1024-2953},
  pages     = {653 -- 674},
  year      = {2014},
  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.},
  language  = {en}
}