Abstract
In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.
| Original language | English |
|---|---|
| Pages (from-to) | 199-219 |
| Number of pages | 21 |
| Journal | Journal of Functional Analysis |
| Volume | 249 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Aug 2007 |
| Externally published | Yes |
Keywords
- Fractional Brownian motion
- Local time
- N-Parameter d-dimensional Brownian motion
- Quasi-sure existence
- Self-intersection local time
- Smooth semimartingale
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Ren, J., & Zhang, X. (2007). Regularity of local times of random fields. Journal of Functional Analysis, 249(1), 199-219. https://doi.org/10.1016/j.jfa.2007.04.017