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 \({\mbox{\boldmath$R$}}^{\nu}\) 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.
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Received: 5 September 1995 / In revised form: 14 March 1996
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Yoshida, M. Construction of infinite dimensional interacting diffusion processes through Dirichlet forms. Probab Theory Relat Fields 106, 265–297 (1996). https://doi.org/10.1007/s004400050065
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DOI: https://doi.org/10.1007/s004400050065
- Mathematics Subject Classification (1991): 60J40, 60J60, 60J70, 60K35