On the existence and the Hölder regularity of the local time of the Brownian bridge

Abstract

Abstract In this paper, we will establish the existence and the Hölder regularity of the local time of the Brownian bridge. Our results are obtained by using a result on Malliavin calculus in [K. Es-Sebaiy, D. Nualart, Y. Ouknine and C. A. Tudor, Occupation densities for certain processes related to fractional Brownian motion, Stochastics 82 2010, 1–3, 133–147] for a Gaussian process with an absolutely continuous random drift, jointly with the classical approach based on the concept of local nondeterminism for Gaussian processes introduced by Berman [S. M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 1973/74, 69–94].