TY  - INPR
A1  - Redig, Frank
A1  - Roelly, Sylvie
A1  - Ruszel, Wioletta
T1  - Short-time Gibbsianness for infinite-dimensional diffusions with space-time interaction
N2  - We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finiterange uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t0 > 0 such that the distribution at time t = t0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 04 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49514
ER  - 
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
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69014
ER  -