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Harmonic measure on 3-dimensional Brownian paths

Published online by Cambridge University Press:  24 October 2008

Krzysztof Burdzy
Krzysztof Burdzy
Affiliation:
University of Washington, Seattle W A 98195, U.S.A.
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Abstract

It is well known that the trace X([0, ∞) of the 3-dimensional Brownian motion X has positive capacity and, therefore, the harmonic measure is well defined on this set. It is shown that a.s., this harmonic measure is singular with respect to the occupation measure Lebesgue ο X−1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 407 - 412
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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