Global heat kernel estimates for symmetric jump processes

Zhen Qing Chen*, Panki Kim, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

80 Citations (Scopus)


In this paper, we study sharp heat kernel estimates for a large class of symmetric jump-type processes in ℝd for all t > 0. A prototype of the processes under consideration are symmetric jump processes on ℝd with jumping intensity where ν is a probability measure on [α1, α2] ⊂ (0, 2), Φ is an increasing function on [0,∞) with β Ie{cyrillic, ukrainian} (0,∞), and c(α, x, y) is a jointly measurable function that is bounded between two positive constants and is symmetric in (x, y). They include, in particular, mixed relativistic symmetric stable processes on ℝd with different masses. We also establish the parabolic Harnack principle.

Original languageEnglish
Pages (from-to)5021-5055
Number of pages35
JournalTransactions of the American Mathematical Society
Issue number9
Publication statusPublished - 2011 Mar 10
Externally publishedYes


  • Dirichlet form
  • Heat kernel estimates
  • Jump process
  • Jumping kernel
  • Parabolic Harnack inequality

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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