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On reflecting diffusion processes and Skorokhod decompositions
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  • Published: September 1993

On reflecting diffusion processes and Skorokhod decompositions

  • Zhen-Qing Chen1 

Probability Theory and Related Fields volume 94, pages 281–315 (1993)Cite this article

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Summary

LetG be ad-dimensional bounded Euclidean domain, H1 (G) the set off in L2(G) such that ∇f (defined in the distribution sense) is in L2(G). Reflecting diffusion processes associated with the Dirichlet spaces (H1(G), ℰ) on L2(G, σdx) are considered in this paper, where

A=(aij is a symmetric, bounded, uniformly ellipticd×d matrix-valued function such thata ij∈H1(G) for eachi,j, and σ∈H1(G) is a positive bounded function onG which is bounded away from zero. A Skorokhod decomposition is derived for the continuous reflecting Markov processes associated with (H1(G), ℰ) having starting points inG under a mild condition which is satisfied when ϖG has finite (d−1)-dimensional lower Minkowski content.

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Authors and Affiliations

  1. Department of Mathematics, Washington University, 63130, St. Louis, MO, USA

    Zhen-Qing Chen

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  1. Zhen-Qing Chen
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Chen, ZQ. On reflecting diffusion processes and Skorokhod decompositions. Probab. Th. Rel. Fields 94, 281–315 (1993). https://doi.org/10.1007/BF01199246

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  • Received: 30 September 1991

  • Revised: 14 April 1992

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01199246

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Mathematics Subject Classification

  • 60 J 60
  • 60 J 60
  • 60 J 65
  • 60 J 55
  • 60 J 35
  • 31 C 25
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