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 $(B_{u{T}_1}/\sqrt{T_1},u\le 1)$ under uniform random sampling.