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

2013/01/01 by Mathieu Rosenbaum, Marc Yor, Rosenbaum, Mathieu +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1311.1900

arxiv created 2013/11/08 · arxiv updated 2013/11/11

Abstract

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.

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