Journal of Applied Mathematics and Stochastic Analysis 
Volume 13 (2000), Issue 2, Pages 125-136
doi:10.1155/S1048953300000149

On the local time density of the reflecting Brownian bridge

Bernhard Gittenberger1 and Guy Louchard2

 1TU Wien, Department of Geometry, Wiedner Hauptstrasse 8-10/113, Wien A-1040, Austria
2Université Libre de Bruxelles, Départemente d'Informatique, -C.P. 212 Campus de la Plaine, Boulevard du Triompher, Bruxelles B-1050, Belgium
Received 1 March 1999; Revised 1 September 1999

Abstract

Expressions for the multi-dimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.