Some explicit formulas for the Brownian bridge, Brownian meander and Bessel process under uniform sampling

Mathieu Rosenbaum (1) , Marc Yor (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 IUF - Institut universitaire de France

We show that simple explicit formulas can be obtained for several relevant quantities related to the laws of the uniformly sampled Brownian bridge, Brownian meander and three dimensional Bessel process. To prove such results, we use the distribution of a triplet of random variables associated to the pseudo-Brownian bridge together with various relationships between the laws of these four processes.

Domaines: Probabilités [math.PR]

Mathieu Rosenbaum, Marc Yor. Some explicit formulas for the Brownian bridge, Brownian meander and Bessel process under uniform sampling. 2013. ⟨hal-00881268⟩