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Pseudo Jordan domains and reflecting Brownian motions
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  • Published: June 1992

Pseudo Jordan domains and reflecting Brownian motions

  • Zhen-Qing Chen1 

Probability Theory and Related Fields volume 94, pages 271–280 (1992)Cite this article

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Summary

The manifold metric between two points in a planar domain is the minimum of the lengths of piecewiseC 1 curves in the domain connecting these two points. We define a bounded simply connected planar region to be a pseudo Jordan domain if its boundary under the manifold metric is topologically homeomorphic to the unit circle. It is shown that reflecting Brownian motionX on a pseudo Jordan domain can be constructed starting at all points except those in a boundary subset of capacity zero.X has the expected Skorokhod decomposition under a condition which is satisfied when ∂G has finite 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. Pseudo Jordan domains and reflecting Brownian motions. Probab. Th. Rel. Fields 94, 271–280 (1992). https://doi.org/10.1007/BF01192446

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  • Received: 05 November 1991

  • Revised: 14 April 1992

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01192446

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Mathematics Subject Classification

  • P 60J65
  • S 31C25
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