Boundary Harnack Principle and Martin Boundary at Infinity for Subordinate Brownian Motions

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticle

Abstract

In this paper we study the Martin boundary of unbounded open sets at infinity for a large class of subordinate Brownian motions. We first prove that, for such subordinate Brownian motions, the uniform boundary Harnack principle at infinity holds for arbitrary unbounded open sets. Then we introduce the notion of κ-fatness at infinity for open sets and show that the Martin boundary at infinity of any such open set consists of exactly one point and that point is a minimal Martin boundary point.

Original languageEnglish (US)
Pages (from-to)407-441
Number of pages35
JournalPotential Analysis
Volume41
Issue number2
DOIs
StatePublished - Jun 2014

Keywords

  • Boundary Harnack principle
  • Harmonic functions
  • Lévy processes
  • Martin boundary
  • Martin kernel
  • Poisson kernel
  • Subordinate Brownian motion

ASJC Scopus subject areas

  • Analysis

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