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Dirichlet spaces and strong Markov processes


Author: Masatoshi Fukushima
Journal: Trans. Amer. Math. Soc. 162 (1971), 185-224
MSC: Primary 60J45
DOI: https://doi.org/10.1090/S0002-9947-1971-0295435-0
MathSciNet review: 0295435
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0295435-0
Keywords: Capacity, regular Dirichlet space, quasi-continuity, equilibrium potential, quasi-homeomorphism, Ray process, Hunt process, fine continuity, hitting probability, reference measure
Article copyright: © Copyright 1971 American Mathematical Society

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