6666
2013
eng
preprint
0
2013-12-16
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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.
urn:nbn:de:kobv:517-opus-69014
6901
MSC - Klassifikation: 60K35 , 60H10
Urheberrechtsschutz
Sylvie Roelly
Wioletta M. Ruszel
Preprints des Instituts für Mathematik der Universität Potsdam
2(2013)18
eng
uncontrolled
infinite-dimensional diffusion
eng
uncontrolled
cluster expansion
eng
uncontrolled
non-Markov drift
eng
uncontrolled
Girsanov formula
eng
uncontrolled
ultracontractivity
Mathematik
open_access
2013
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/6666/premath18_2013.pdf