TY  - JOUR
A1  - Rœlly, Sylvie
A1  - Zass, Alexander
T1  - Marked Gibbs point processes with unbounded interaction
BT  - An existence result
JF  - Journal of statistical physics
N2  - We construct marked Gibbs point processes in R-d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks-attached to the locations in R-d-belong to a general normed space G. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.
KW  - Marked Gibbs process
KW  - Infinite-dimensional interacting diffusion
KW  - Specific entropy
KW  - DLR equation
Y1  - 2020
U6  - https://doi.org/10.1007/s10955-020-02559-3
SN  - 0022-4715
SN  - 1572-9613
VL  - 179
IS  - 4
SP  - 972
EP  - 996
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Dereudre, David
A1  - Roelly, Sylvie
T1  - Path-dependent infinite-dimensional SDE with non-regular drift
BT  - an existence result
JF  - Annales de l'Institut Henri Poincaré : B, Probability and statistics
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 bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. 
The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift.
N2  - Nous établissons, dans cet article, l’existence de solutions faibles pour un système infini-dimensionnel de diffusions browniennes. Le terme de dérive est véritablement général, au sens où il est supposé n’être ni borné, ni continu, ni Markovien. Nous supposons cependant que la loi initiale admet une entropie spécifique finie.
L’originalité de notre méthode consiste en l’utilisation de la bornitude de l’entropie spécifique comme critère de tension et en l’identification des solutions du système comme solutions d’un problème variationnel sur l’espace des trajectoires. Notre résultat améliore clairement ceux préexistants concernant des dynamiques libres perturbées par des dérives bornées.
KW  - Infinite-dimensional SDE
KW  - Non-Markov drift
KW  - Non-regular drift
KW  - Variational principle
KW  - Specific entropy
Y1  - 2017
U6  - https://doi.org/10.1214/15-AIHP728
SN  - 0246-0203
VL  - 53
IS  - 2
SP  - 641
EP  - 657
PB  - Inst. of Mathematical Statistics
CY  - Bethesda
ER  -