Abstract.
In this paper, we will give sufficient conditions for the existence of the reflecting diffusion process on a locally compact space. In constructing reflecting diffusion process, we consider the corresponding Martin–Kuramochi boundary as the reflecting barrier and introduce the notion of strong (ℰ, u)-Caccioppoli set. Our method covers reflecting diffusion processes with diffusion coefficient degenerating on the boundary.
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Received: 23 June 1997 / Revised version: 28 September 1991/ Published online: 14 June 2000
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Kaneko, H. Martin–Kuramochi boundary and reflecting symmetric diffusion. Probab Theory Relat Fields 117, 533–550 (2000). https://doi.org/10.1007/PL00008734
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DOI: https://doi.org/10.1007/PL00008734