JournalsrmiVol. 34, No. 2pp. 541–592

Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces

  • Panki Kim

    Seoul National University, Republic of Korea
  • Renming Song

    University of Illinois at Urbana-Champaign, USA and Nankai University, Tianjin, China
  • Zoran Vondraček

    University of Zagreb, Croatia and University of Illinois, Urbana, USA
Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces cover

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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 \infty is accessible from an open set DD, then there is only one Martin boundary point of DD 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.

Cite this article

Panki Kim, Renming Song, Zoran Vondraček, Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 541–592

DOI 10.4171/RMI/995