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
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
Copyright © 2000 Bernhard Gittenberger and Guy Louchard. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.