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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the excursion process of Brownian motion


Author: Frank B. Knight
Journal: Trans. Amer. Math. Soc. 258 (1980), 77-86
MSC: Primary 60J65; Secondary 60J55
DOI: https://doi.org/10.1090/S0002-9947-1980-0554319-6
MathSciNet review: 554319
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Abstract: Let $W_0^ + (t)$ denote the scaled excursion process of Brownian motion, and let $l_0^ + (a), 0 \leqslant a,$ be its local time at a. The joint distribution of $l_0^ + (a), \beta (a),$ and $\gamma (a)$ is obtained, where $\beta (a)$ and $\gamma (a)$ are the last exit time and the first passage time of a by $W_0^{ + } (t)$.


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Article copyright: © Copyright 1980 American Mathematical Society