Path continuity of fractional Dirichlet functionals

We prove that the quasi continuous version of a functional in E-r(p) is continuous along the sample paths.of the Dirichlet process provided that p > 2, 0 < r less than or equal to 1 and pr > 2, without assuming the Meyer equivalence. Parallel results for multi-parameter processes are also obtained. Moreover, for 1 < p < 2, we prove that a n parameter Dirichlet process does not touch a set of (p, 2n)-zero capacity. As an example, we also study the quasi-everywhere existence of the local times of martingales on path space. (C) 2003 Editions scientifiques et medicales Elsevier SAS.All rights reserved.