摘要
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.
| 源语言 | 英语 |
|---|---|
| 页（从-至） | 27-62 |
| 页数 | 36 |
| 期刊 | Stochastic Processes and their Applications |
| 卷 | 108 |
| 期 | 1 |
| DOI | |
| 出版状态 | 已出版 - 1 11月 2003 |
| 已对外发布 | 是 |
指纹
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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