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

• Panki Kim ^[1] ; Renming Song ^[2] ; Zoran Vondraček ^[3]
  1. [1] Seoul National University

     Seoul National University

     Corea del Sur

     
  2. [2] University of Illinois at Urbana Champaign

     University of Illinois at Urbana Champaign

     Township of Cunningham, Estados Unidos

     
  3. [3] University of Zagreb

     University of Zagreb

     Croacia

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 2, 2018, págs. 541-592
• Idioma: inglés
• DOI: 10.4171/RMI/995
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.