Minimal thinness for subordinate Brownian motion in half-space

Panki Kim[1]; Renming Song[2]; Zoran Vondraček[3]

  • [1] Department of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 151-747, Republic of Korea
  • [2] Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
  • [3] Department of Mathematics, University of Zagreb, Zagreb, Croatia

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 1045-1080
  • ISSN: 0373-0956

Abstract

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We study minimal thinness in the half-space H : = { x = ( x ˜ , x d ) : x ˜ ∈ ℝ d - 1 , x d > 0 } for a large class of subordinate Brownian motions. 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.

How to cite

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Kim, Panki, Song, Renming, and Vondraček, Zoran. "Minimal thinness for subordinate Brownian motion in half-space." Annales de l’institut Fourier 62.3 (2012): 1045-1080. <http://eudml.org/doc/251076>.

@article{Kim2012,
abstract = {We study minimal thinness in the half-space $H:=\lbrace x=(\widetilde\{x\}, x_d):\, \widetilde\{x\}\in \mathbb\{R\}^\{d-1\}, x_d&gt;0\rbrace $ for a large class of subordinate Brownian motions. 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.},
affiliation = {Department of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 151-747, Republic of Korea; Department of Mathematics, University of Illinois, Urbana, IL 61801, USA; Department of Mathematics, University of Zagreb, Zagreb, Croatia},
author = {Kim, Panki, Song, Renming, Vondraček, Zoran},
journal = {Annales de l’institut Fourier},
keywords = {Minimal thinness; subordinate Brownian motion; boundary Harnack principle; Green function; Martin kernel; minimal thinness},
language = {eng},
number = {3},
pages = {1045-1080},
publisher = {Association des Annales de l’institut Fourier},
title = {Minimal thinness for subordinate Brownian motion in half-space},
url = {http://eudml.org/doc/251076},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Kim, Panki
AU - Song, Renming
AU - Vondraček, Zoran
TI - Minimal thinness for subordinate Brownian motion in half-space
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 1045
EP - 1080
AB - We study minimal thinness in the half-space $H:=\lbrace x=(\widetilde{x}, x_d):\, \widetilde{x}\in \mathbb{R}^{d-1}, x_d&gt;0\rbrace $ for a large class of subordinate Brownian motions. 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.
LA - eng
KW - Minimal thinness; subordinate Brownian motion; boundary Harnack principle; Green function; Martin kernel; minimal thinness
UR - http://eudml.org/doc/251076
ER -

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