Dirichlet spaces and strong Markov processes

Fukushima, Masatoshi

doi:10.1090/S0002-9947-1971-0295435-0

Dirichlet spaces and strong Markov processes
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by Masatoshi Fukushima

Trans. Amer. Math. Soc. 162 (1971), 185-224

DOI: https://doi.org/10.1090/S0002-9947-1971-0295435-0

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Abstract:

We show that there exists a suitable strong Markov process on the underlying space of each regular Dirichlet space. Potential theoretic concepts due to A. Beurling and J. Deny are then described in terms of the associated strong Markov process. The proof is carried out by developing potential theory for Dirichlet spaces and symmetric Ray processes and by using a method of transformation of underlying spaces.

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