Minimal thinness for subordinate Brownian motion in half space

Abstract

We study minimal thinness in the half-space $H:=\{x=(\wt{x}, x_d):\, \wt{x}\in \R^{d-1}, x_d>0\}$ for a large class of rotationally invariant Lévy processes, including symmetric stable processes and sums of Brownian motion and independent stable processes. We show that the same test for the minimal thinness of a subset of $H$ below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.

31 pages

References in corpus (2)

• Potential Theory of Subordinate Brownian Motions Revisited
• Global Heat Kernel Estimates for $\Delta +{\Delta }^{\alpha /2}$ in Half-space-like domains

Cited by in corpus (1)

• Global Heat Kernel Estimates for $\Delta +{\Delta }^{\alpha /2}$ in Half-space-like domains