Boundary Harnack principle for subordinate Brownian motions

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in κ-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded κ-fat open sets with respect to these processes with their Euclidean boundaries.

Original languageEnglish (US)
Pages (from-to)1601-1631
Number of pages31
JournalStochastic Processes and their Applications
Volume119
Issue number5
DOIs
StatePublished - May 2009

Keywords

  • Bernstein functions
  • Boundary Harnack principle
  • Complete Bernstein functions
  • Green functions
  • Harmonic functions
  • Harnack inequality
  • Martin boundary
  • Mixture of symmetric stable processes
  • Poisson kernels
  • Subordinate Brownian motion
  • Subordinator
  • Symmetric stable processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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