Abstract
We prove that the quasi continuous version of a functional in Epr 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.
Original language | English |
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Pages (from-to) | 368-378 |
Number of pages | 11 |
Journal | Bulletin des Sciences Mathematiques |
Volume | 127 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jun 2003 |
Externally published | Yes |
Keywords
- Capacity
- Dirichlet forms
- Path continuity
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Ren, J., & Zhang, X. (2003). Path continuity of fractional Dirichlet functionals. Bulletin des Sciences Mathematiques, 127(4), 368-378. https://doi.org/10.1016/S0007-4497(03)00029-0