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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 6, Fasc. 1,
pages 11 - 17
 

SKOROKHOD PROBLEM - ELEMENTARY PROOF OF THE AZEMA-YOR FORMULA

Piotr Zaremba

Abstract: Let m be a centered probability measure with the finite second moment. Let the stopping time T for the Brownian motion W be defined as

T = inf(t > 0;Y(W ) < sup W ), t 0<s<t s
where Y is a barycenter function of measure m. Azema and Yor [1] have shown that WT has then the distribution m and integral 2 ET = x md(x). This paper contains an elementary proof of this result.

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

Key words and phrases: -

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