On the Estimates of the Density of Feynman-Kac Semigroups of $α$-Stable-like Processes
| dc.creator | Wang, Chunlin | |
| dc.date | 2006-11-19 | |
| dc.date.accessioned | 2026-07-07T07:33:06Z | |
| dc.date.available | 2026-07-07T07:33:06Z | |
| dc.description | Suppose that $α\in (0,2)$ and that $X$ is an $α$-stable-like process on $\R^d$. Let $F$ be a function on $\R^d$ belonging to the class $\bf{J_{d,α}}$ (see Introduction) and $A_{t}^{F}$ be $\sum_{s \le t}F(X_{s-},X_{s}), t> 0$, a discontinuous additive functional of $X$. With neither $F$ nor $X$ being symmetric, under certain conditions, we show that the Feynman-Kac semigroup $\{S_{t}^{F}:t \ge 0\}$ defined by $$ S_{t}^{F}f(x)=\mathbb{E}_{x}(e^{-A_{t}^{F}}f(X_{t}))$$ has a density $q$ and that there exist positive constants $C_1,C_2,C_3$ and $C_4$ such that $$C_{1}e^{-C_{2}t}t^{-\frac{d}α}(1 \wedge \frac{t^{\frac{1}α}}{|x-y|})^{d+α} \leq q(t,x,y) \leq C_{3}e^{C_{4}t}t^{-\frac{d}α}(1 \wedge \frac{t^{\frac{1}α}}{|x-y|})^{d+α}$$ for all $(t,x,y)\in (0,\infty) \times \R^d \times \R^d$. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611565 | |
| dc.identifier | http://arxiv.org/abs/math/0611565 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119338 | |
| dc.subject | Probability | |
| dc.subject | Primary 60J45, 60J35; Secondary 60J55, 60J75, 60G51, 60G52 | |
| dc.title | On the Estimates of the Density of Feynman-Kac Semigroups of $α$-Stable-like Processes | |
| dc.type | text |