TY  - JOUR
A1  - Roelly, Sylvie
A1  - Ruszel, W. M.
T1  - Propagation of gibbsianness for infinite-dimensional diffusions with space-time interaction
JF  - Markov processes and related fields
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.
KW  - infinite-dimensional diffusion
KW  - cluster expansion
KW  - non-Markov drift
KW  - Girsanov formula
KW  - ultracontractivity
KW  - planar rotors
Y1  - 2014
SN  - 1024-2953
VL  - 20
IS  - 4
SP  - 653
EP  - 674
PB  - Polymat
CY  - Moscow
ER  - 
TY  - INPR
A1  - Dereudre, David
A1  - Roelly, Sylvie
T1  - Path-dependent infinite-dimensional SDE with non-regular drift : an existence result
N2  - We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)11 
KW  - Infinite-dimensional SDE
KW  - non-Markov drift
KW  - non-regular drift
KW  - variational principle
KW  - specific entropy
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72084
SN  - 2193-6943
VL  - 3
IS  - 11
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -