Heat kernel estimates for stable-like processes on d-sets

Zhen Qing Chen; Takashi Kumagai

doi:10.1016/S0304-4149(03)00105-4

Heat kernel estimates for stable-like processes on d-sets

Zhen Qing Chen, Takashi Kumagai^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

300 Citations (Scopus)

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	https://doi.org/10.1016/S0304-4149(03)00105-4
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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10.1016/S0304-4149(03)00105-4

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AB - 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.

KW - Besov spaces

KW - Heat kernels

KW - Jump processes

KW - Lévy systems

KW - Parabolic Harnack inequality

KW - Stable-like processes

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SP - 27

EP - 62

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Heat kernel estimates for stable-like processes on d-sets

Abstract

Keywords

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