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Construction of infinite dimensional interacting diffusion processes through Dirichlet forms

Research paper by Minoru W. Yoshida

Indexed on: 01 Oct '96Published on: 01 Oct '96Published in: Probability Theory and Related Fields



Abstract

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 \({\mbox{\boldmath$R$}}^{\nu}\) 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.