Minimal thinness for subordinate Brownian motion in half space

Details Minimal thinness for subordinate Brownian motion in half space Minimal thinness for subordinate Brownian motion in half space

2010-10-04

arxiv.org/abs/1010.0662v2

Mathematics

Probability

31 pages

Scientific paper

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 L\'evy 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.

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