Abstract
In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C1,1 open sets in ℝd, where d ≥ 1 and α ε (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C1,1 open sets.
| Original language | English |
|---|---|
| Pages (from-to) | 361-399 |
| Number of pages | 39 |
| Journal | Probability Theory and Related Fields |
| Volume | 146 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Dec 2009 |
| Externally published | Yes |
Keywords
- Boundary Harnack principle
- Censored stable process
- Censored stable-like process
- Exit time
- Fractional Laplacian
- Green function
- Heat kernel
- Intrinsic ultracontractivity
- Lévy system
- Parabolic Harnack principle
- Symmetric stable-like process
- Symmetric α-stable process
- Transition density
- Transition density function
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Chen, Z. Q., Kim, P., & Song, R. (2009). Two-sided heat kernel estimates for censored stable-like processes. Probability Theory and Related Fields, 146(3), 361-399. https://doi.org/10.1007/s00440-008-0193-3