Minimal thinness for subordinate Brownian motion in half-space

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review


We study minimal thinness in the half-space H:= {x = (x̃, x d): x̃ ∈ ℝ d-1,x d > 0} for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of H below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.

Original languageEnglish (US)
Pages (from-to)1045-1080
Number of pages36
JournalAnnales de l'Institut Fourier
Issue number3
StatePublished - 2012


  • Boundary harnack principle
  • Green function
  • Martin kernel
  • Minimal thinness
  • Subordinate Brownian motion

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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