Two-sided heat kernel estimates for censored stable-like processes

Zhen Qing Chen, Panki Kim, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C 1,1 open sets in ℝ d , where d ≥ 1 and α ε (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C 1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C 1,1 open sets.

Original languageEnglish (US)
Pages (from-to)361-399
Number of pages39
JournalProbability Theory and Related Fields
Volume146
Issue number3
DOIs
StatePublished - Dec 1 2009

Keywords

  • Boundary Harnack principle
  • Censored stable process
  • Censored stable-like process
  • Exit time
  • Fractional Laplacian
  • Green function
  • Heat kernel
  • Intrinsic ultracontractivity
  • Lévy system
  • Parabolic Harnack principle
  • Symmetric stable-like process
  • Symmetric α-stable process
  • Transition density
  • Transition density function

ASJC Scopus subject areas

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

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