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 be an unbounded open set. Infinity is accessible from if the expected exit time from 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 . Similar results are also proved for finite boundary points of .
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