Abstract
The notion of d-set arises in the theory of function spaces and in fractal geometry. Geometrically self-similar sets are typical examples of d-sets. In this paper stable-like processes on d-sets are investigated, which include reflected stable processes in Euclidean domains as a special case. More precisely, we establish parabolic Harnack principle and derive sharp two-sided heat kernel estimate for such stable-like processes. Results on the exact Hausdorff dimensions for the range of stable-like processes are also obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 27-62 |
| Number of pages | 36 |
| Journal | Stochastic Processes and their Applications |
| Volume | 108 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Nov 2003 |
| Externally published | Yes |
Keywords
- Besov spaces
- Heat kernels
- Jump processes
- Lévy systems
- Parabolic Harnack inequality
- Stable-like processes
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Chen, Z. Q., & Kumagai, T. (2003). Heat kernel estimates for stable-like processes on d-sets. Stochastic Processes and their Applications, 108(1), 27-62. https://doi.org/10.1016/S0304-4149(03)00105-4