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Martin–Kuramochi boundary and reflecting symmetric diffusion
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  • Published: August 2000

Martin–Kuramochi boundary and reflecting symmetric diffusion

  • Hiroshi Kaneko1 

Probability Theory and Related Fields volume 117, pages 533–550 (2000)Cite this article

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Science University of Tokyo, 26 Wakamiya, Shinjuku, Tokyo, Japan. e-mail: stochos@rs.kagu.sut.ac.jp, , , , , , JP

    Hiroshi Kaneko

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  1. Hiroshi Kaneko
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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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  • Issue Date: August 2000

  • DOI: https://doi.org/10.1007/PL00008734

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  • Mathematics Subject Classification (1991): 60J60, 60J55, 31C25, 31C35
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