Accessibility, martin boundary and minimal thinness for feller processes in metric measure spaces

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticle

Abstract

In this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes in metric measure spaces. We show that if ∞ is accessible from an open set D, then there is only one Martin boundary point of D associated with it, and this point is minimal. We also prove the analogous result for finite boundary points. As a consequence, we show that minimal thinness of a set is a local property.

Original languageEnglish (US)
Pages (from-to)541-592
Number of pages52
JournalRevista Matematica Iberoamericana
Volume34
Issue number2
DOIs
StatePublished - Jan 1 2018

Keywords

  • Martin boundary
  • Martin kernel
  • Minimal thinness
  • Purely discontinuous Feller process

ASJC Scopus subject areas

  • Mathematics(all)

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