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

@article{Kim2015AccessibilityMB,
  title={Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces},
  author={P. Kim and R. Song and Z. Vondravcek},
  journal={arXiv: Probability},
  year={2015}
}
  • P. Kim, R. Song, Z. Vondravcek
  • Published 2015
  • Mathematics
  • arXiv: Probability
  • In this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes on metric measure spaces. We show that if $\infty$ 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. 
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