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Transactions of the American Mathematical Society

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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0554319-6
Article copyright: © Copyright 1980 American Mathematical Society

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