Path continuity of fractional Dirichlet functionals

✍ Scribed by Jiagang Ren; Xicheng Zhang

• Publisher: Elsevier Science
• Year: 2003
• Tongue: French
• Weight: 108 KB
• Volume: 127
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/s0007-4497(03)00029-0

✦ Synopsis

We prove that the quasi continuous version of a functional in E p r is continuous along the sample paths of the Dirichlet process provided that p > 2, 0 < r 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.