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Z. Vondraček

Publications and source records attributed to Z. Vondraček.

3 recordsLinked to original sources
arXiv2016

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

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.

math.PR↗
arXiv2016

Martin boundary of unbounded sets for purely discontinuous Feller processes

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

math.PR↗