Sharp heat kernel estimates for relativistic stable processes in open sets

Zhen Qing Chen, Panki Kim, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m - (m 2/α - {increment}) α/2] in C 1,1 open sets. Here m > 0 and α ∈ (0, 2). The estimates are uniform in m ∈ (0, M] for each fixed M > 0. Letting m ↓ 0, we recover the Dirichlet heat kernel estimates for {increment} α/2 := -(-{increment}) α/2 in C 1,1 open sets obtained in [14]. Sharp two-sided estimates are also obtained for Green functions of relativistic stable processes in bounded C 1,1 open sets.

Original languageEnglish (US)
Pages (from-to)213-244
Number of pages32
JournalAnnals of Probability
Volume40
Issue number1
DOIs
StatePublished - Jan 2012

Keywords

  • Exit time
  • Green function
  • Heat kernel
  • Lèvy system
  • Parabolic Harnack inequality
  • Relativistic stable process
  • Symmetric α-stable process
  • Transition density

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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