Representations for continuous additive functionals of super-Brownian and super-stable processes
β Scribed by Stephen M. Krone
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 546 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
We study a class of continuous additive functionals for super-Brownian and super-stable processes. These are given in terms of a Tanaka-like formula that generalizes the one for local times. We give representations for these additive functionals in terms of the corresponding local times. As an example, we discuss fractional Laplacians of super-Brownian local times.
π SIMILAR VOLUMES
## Abstract Let __X~t~__ be a symmetric stable process on __d__βdimensional Euclidean space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {R}}^d$\end{document}. Let __F__(__x__, __y__) be a symmetric positive bounded function on \documentclass{article}\usepac
Martin boundaries and integral representations of positive functions which are harmonic in a bounded domain D with respect to Brownian motion are well understood. Unlike the Brownian case, there are two different kinds of harmonicity with respect to a discontinuous symmetric stable process. One kind