Heat kernel estimates for jump processes of mixed types on metric measure spaces

Zhen Qing Chen*, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

177 Citations (Scopus)

Abstract

In this paper, we investigate symmetric jump-type processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces. The class of metric measure spaces includes the Alfors d-regular sets, which is a class of fractal sets that contains geometrically self-similar sets. A typical example of our jump-type processes is the symmetric jump process with jumping intensity e-c0 (x, y)|x-y|}, ∫α1α2} c(α, x, y)|x-y|d+α}, ν (dα) where ν is a probability measure on [α1, α2]subset (0, 2), c(α, x, y) is a jointly measurable function that is symmetric in (x, y) and is bounded between two positive constants, and c 0(x, y) is a jointly measurable function that is symmetric in (x, y) and is bounded between γ1 and γ2, where either γ2 gamma;1 > 0 or γ1 = γ2 = 0. This example contains mixed symmetric stable processes on Rn as well as mixed relativistic symmetric stable processes on Rn. We establish parabolic Harnack principle and derive sharp two-sided heat kernel estimate for such jump-type processes.

Original languageEnglish
Pages (from-to)277-317
Number of pages41
JournalProbability Theory and Related Fields
Volume140
Issue number1-2
DOIs
Publication statusPublished - 2008 Jan
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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