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 Electronic Journal of Probability > Vol. 9 (2004) > Paper 27 open journal systems 


The Beurling Estimate for a Class of Random Walks

Gregory F Lawler, Cornell University
Vlada Limic, University of British Columbia


Abstract
An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -&epsilon reaches the unit circle without hitting the curve is bounded above by c &epsilon^{1/2}. This estimate is very useful in analysis of boundary behavior of conformal maps, especially for connected but rough boundaries. The corresponding estimate for simple random walk was first proved by Kesten. In this note we extend this estimate to random walks with zero mean, finite (3+&delta)-moment.


Full text: PDF

Pages: 846-861

Published on: December 13, 2004


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Electronic Journal of Probability. ISSN: 1083-6489