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On reflected Dirichlet spaces. (English) Zbl 0767.60073
Summary: Reflecting diffusion processes on smooth domains in Euclidean space are well understood. M. L. Silverstein [Ill. J. Math. 18, No. 2, 310- 355 (1974; Zbl 0303.60066) and Symmetric Markov processes (1974; Zbl 0296.60038)] developed two variant procedures for constructing the reflected processes for a general class of symmetric Hunt processes from a Dirichlet space point of view. A direct approach is given in this paper and these two variant procedures are shown to yield the same result. Only the techniques of martingales and ordinary Markov processes are used.

MSC:
60J60 Diffusion processes
60G44 Martingales with continuous parameter
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