On the potential theory of one-dimensional subordinate Brownian motions with continuous components

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that S is a subordinator with a nonzero drift and W is an independent 1-dimensional Brownian motion. We study the subordinate Brownian motion X defined by Xt = W(St). We give sharp bounds for the Green function of the process X killed upon exiting a bounded open interval and prove a boundary Harnack principle. In the case when S is a stable subordinator with a positive drift, we prove sharp bounds for the Green function of X in (0, ∞), and sharp bounds for the Poisson kernel of X in a bounded open interval.

Original languageEnglish (US)
Pages (from-to)153-173
Number of pages21
JournalPotential Analysis
Volume33
Issue number2
DOIs
StatePublished - Aug 2010

Keywords

  • Boundary Harnack principle
  • Green function
  • Poisson kernel
  • Subordinate Brownian motion
  • Subordinator

ASJC Scopus subject areas

  • Analysis

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