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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 8, Fasc. ,
pages 49 - 52
 

CONVERGENCE OF 2-DIMENSIONAL h -PROCESSES

Krzysztof Burdzy

Abstract: Suppose that D < C is a simply connected domain and p is a minimal Martin boundary point. Assume that there exists a curve in D which converges to p in the Martin topology and to z (- C in the Euclidean topology. Then the same holds for almost all h -paths, where h is a minimal harmonic function represented by p. In such a case almost all h -paths have finite lifetime. This permits to define a Brownian excursion law in D starting from such a point p.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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