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

Zhen Qing Chen, Takashi Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

277 Citations (Scopus)


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 languageEnglish
Pages (from-to)27-62
Number of pages36
JournalStochastic Processes and their Applications
Issue number1
Publication statusPublished - 2003 Nov 1
Externally publishedYes


  • Besov spaces
  • Heat kernels
  • Jump processes
  • Lévy systems
  • Parabolic Harnack inequality
  • Stable-like processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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