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Generalized Markov fields and Dirichlet forms. (English) Zbl 0588.60044

The author considers a generalized Gaussian random field on a topological space for which the random field is indexed by measures and its covariance function is given by a transient Dirichlet form. He shows that this random field has the Markov property if and only if the Dirichlet form has the local property, by using potential theoretical methods. A similar result is shown in E. B. Dynkin [Bull. Am. Math. Soc., New Ser. 3, 975-999 (1980; Zbl 0519.60046)].
Reviewer: S.Kusuoka

MSC:

60G60 Random fields
31C25 Dirichlet forms
60J45 Probabilistic potential theory
81T99 Quantum field theory; related classical field theories

Citations:

Zbl 0519.60046
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References:

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