Pseudo Jordan domains and reflecting Brownian motions

Zhen Qing Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

The manifold metric between two points in a planar domain is the minimum of the lengths of piecewise C1 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 motion X 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.

Original languageEnglish
Pages (from-to)271-280
Number of pages10
JournalProbability Theory and Related Fields
Volume94
Issue number2
DOIs
Publication statusPublished - Jun 1992
Externally publishedYes

Keywords

  • Mathematics Subject Classification: P 60J65, S 31C25

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