Green function estimates and Harnack inequality for subordinate Brownian motions

Murali Rao, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

Let X be a Lévy process in ℝd, d ≥ 3, obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Lévy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the Lévy measure of the subordinator we prove that the Harnack inequality is valid for the nonnegative harmonic functions of X.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalPotential Analysis
Volume25
Issue number1
DOIs
StatePublished - Aug 2006

Keywords

  • Capacity
  • Complete Bernstein function
  • Green function
  • Harnack inequality
  • Subordinate Brownian motion
  • Subordinator

ASJC Scopus subject areas

  • Analysis

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