Minimal thinness for subordinate Brownian motion in half-space

DOI10.5802/AIF.2716zbMATH Open1273.60096arXiv1010.0662OpenAlexW2963215998MaRDI QIDQ714923

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Publication date: 12 October 2012

Published in: (Search for Journal in Brave)

Abstract: We study minimal thinness in the half-space

H : = x = (w t x, x_{d}) :, w t x i n 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.

Full work available at URL: https://arxiv.org/abs/1010.0662

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