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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]. [ABSTRACT FROM AUTHOR]

In this paper we introduce and study a self-similar Gaussian process denoted by with parameters and . This process generalizes the well-known fractional Brownian motion introduced by Mandelbrot and Van Ness [SIAM Rev. 10 (1968), no. 4, 422-437], the sub-fractional Brownian motion introduced by Bojdecki, Gorostiza and Talarczyket [Statist. Probab. Lett. 69 (2004), 405-419] and the Gaussian process introduced by Lei and Nualart [Statist. Probab. Lett. 79 (2009), 619-624] in order to obtain a decomposition in law of the bifractional Brownian motion. [ABSTRACT FROM AUTHOR]