Construction of infinite dimensional interacting diffusion processes through Dirichlet forms

Summary. By the theory of quasi-regular Dirichletforms and the associated special standard processes, the existence of symmetric diffusion processes taking values in the space of non-negative integer valued Radon measures on and having Gibbs invariant measures associated with some given pair potentials is considered. The existence of such diffusions can be shown for a wide class of potentials involving some singular ones. Also, as a consequence of an application of stochastic calculus, a representation for the diffusion by means of a stochastic differential equation is derived. Received: 5 September 1995 / In revised form: 14 March 1996