Path continuity of fractional Dirichlet functionals

Jiagang Ren*, Xicheng Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
Plum Print visual indicator of research metrics
  • Citations
    • Citation Indexes: 5
  • Captures
    • Readers: 3
see details

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 languageEnglish
Pages (from-to)368-378
Number of pages11
JournalBulletin des Sciences Mathematiques
Volume127
Issue number4
DOIs
Publication statusPublished - Jun 2003
Externally publishedYes

Keywords

  • Capacity
  • Dirichlet forms
  • Path continuity

Fingerprint

Dive into the research topics of 'Path continuity of fractional Dirichlet functionals'. Together they form a unique fingerprint.

Cite this

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