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 language | English |
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Pages (from-to) | 271-280 |
Number of pages | 10 |
Journal | Probability Theory and Related Fields |
Volume | 94 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 1992 |
Externally published | Yes |
Keywords
- Mathematics Subject Classification: P 60J65, S 31C25