Minimal thinness with respect to subordinate killed Brownian motions

TL;DR

This paper develops criteria to determine when a set is minimally thin at a boundary point for a broad class of subordinate killed Brownian motions in various domains, advancing understanding of boundary behavior in stochastic processes.

Contribution

It introduces new tests for minimal thinness applicable to subordinate killed Brownian motions in diverse domain types, expanding theoretical tools in potential theory.

Findings

Provided criteria for minimal thinness at boundary points.

Extended analysis to various domain geometries.

Enhanced understanding of boundary behavior in stochastic processes.

Abstract

Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness for a large class of subordinate killed Brownian motions in bounded C1,1 domains, C1,1 domains with compact complements and domains above graphs of bounded C1,1 functions.