Equilibrium diffusion on the cone of discrete radon measures
Let denote the cone of discrete Radon measures on . There is a natural differentiation on : for a differentiable function , one defines its gradient as a vector field which assigns to each an element of a tangent space to at point eta. Let be a potential of pair interaction, and let mu be a corresponding Gibbs perturbation of (the distribution of) a completely random measure on . In particular, mu is a probability measure on such that the set of atoms of a discrete measure is mu-a.s. dense in . We consider the corresponding Dirichlet form Integrating by parts with respect to the measure mu, we explicitly find the generator of this Dirichlet form. By using the theory of Dirichlet forms, we prove the main result of the paper: If d a parts per thousand yen 2, there exists a conservative diffusion process on which is properly associated with the Dirichlet form .
44
1
71-90
71-90
Springer