A support property for infinite dimensional interacting diffusion processes

Abstract

The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space $\ddot{\Gamma }=$ $\{Z_{+}$-valued Radon measures on $\IR^d\}$. We show that under mild conditions, the set $\ddot{\Gamma }\setminus \Gamma$ is $\e$-exceptional, where $\Gamma$ is the space of locally finite configurations in $\IR^d$, that is, measures $\gamma \in \ddot{\Gamma }$ satisfying $\sup_{x\in\IR^d}γ(\{x\})\leq 1$. Thus, the associated diffusion lives on the smaller space $\Gamma$. This result also holds for Gibbs measures with superstable interactions.

French title: Une propriété de support pour des processus de diffusion en dimension infinie avec interaction

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