English

Martin boundary of unbounded sets for purely discontinuous Feller processes

Probability 2016-11-17 v4

Abstract

In this paper, we study the Martin kernels of general open sets associated with inaccessible points for a large class of purely discontinuous Feller processes in metric measure spaces. Let DD be an unbounded open set. Infinity is accessible from DD if the expected exit time from DD is infinite, and inaccessible otherwise. We prove that under suitable assumptions there is only one Martin boundary point associated with infinity, and that this point is minimal if and only if infinity is accessible from DD. Similar results are also proved for finite boundary points of DD.

Keywords

Cite

@article{arxiv.1510.04574,
  title  = {Martin boundary of unbounded sets for purely discontinuous Feller processes},
  author = {P. Kim and R. Song and Z. Vondraček},
  journal= {arXiv preprint arXiv:1510.04574},
  year   = {2016}
}

Comments

Definition of the infinite Martin boundary point modified; Corollary 1.5 added; 26 pages. arXiv admin note: text overlap with arXiv:1510.04571