Harmonic measures for symmetric stable processes

Jang Mei Wu

Research output: Contribution to journalArticlepeer-review

Abstract

Let D be an open set in ℝn (n ≥ 2) and ω(., D) be the harmonic measure on Dc with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set 5 on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and Dc \ S that determine whether ω(S, D) is zero or positive.

Original languageEnglish (US)
Pages (from-to)281-293
Number of pages13
JournalStudia Mathematica
Volume149
Issue number3
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)

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