TY - INPR
A1 - Roelly, Sylvie
A1 - Ruszel, Wioletta M.
T1 - Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction
N2 - 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.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)18
KW - infinite-dimensional diffusion
KW - cluster expansion
KW - non-Markov drift
KW - Girsanov formula
KW - ultracontractivity
Y1 - 2013
UR - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/6666
UR - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-69014
ER -