Green function estimates for relativistic stable processes in half-space-like 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 Green functions of relativistic stable processes (i.e. Green functions for non-local operators m-(m2/α-Δ)α/2) in half-space-like C1,1 open sets. The estimates are uniform in m∈(0,M] for each fixed M ∈ (0,∞). When m ↓ 0, our estimates reduce to the sharp Green function estimates for -(-Δ) α/2 in such kind of open sets that were obtained recently in Chen and Tokle [12]. As a tool for proving our Green function estimates, we show that a boundary Harnack principle for Xm, which is uniform for all m ∈ (0,∞), holds for a large class of non-smooth open sets.

Original languageEnglish (US)
Pages (from-to)1148-1172
Number of pages25
JournalStochastic Processes and their Applications
Volume121
Issue number5
DOIs
StatePublished - May 2011

Keywords

  • Exit time
  • Green function
  • Lévy system
  • Relativistic stable process
  • Symmetric α-stable process
  • Uniform Harnack inequality
  • Uniform boundary Harnack principle

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Green function estimates for relativistic stable processes in half-space-like open sets'. Together they form a unique fingerprint.

Cite this