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## On the law of a triplet associated with the pseudo-Brownian bridge

### Abstract

We identify the distribution of a natural triplet associated with the pseudo-Brownian bridge. In particular, for $B$ a Brownian motion and $T_1$ its first hitting time of the level one, this remarkable law allows us to understand some properties of the process $(B_{uT_1}/\sqrt{T_1},~u\leq 1)$ under uniform random sampling

Topics: Brownian motion, pseudo-Brownian bridge, Bessel process, local time, hitting times, scaling, uniform sampling, Mellin transform, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2013
OAI identifier: oai:HAL:hal-00877162v1
Provided by: Hal-Diderot

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