Pseudo Jordan domains and reflecting Brownian motions |
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Authors: | Zhen-Qing Chen |
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Institution: | (1) Department of Mathematics, Washington University, 63130 St. Louis, MO, USA |
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Abstract: | 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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Keywords: | P 60J65 S 31C25 |
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