no. 3
Minimal thinness for subordinate Brownian motion in half-space
Kim, Panki1; Song, Renming2; Vondraček, Zoran3
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, Volume 62 (2012) no. 3, pp. 1045-1080.

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.

Nous étudions l’effilement minimal dans le demi-espace H:={x=(x ˜,x d ):x ˜∈ℝ d-1 ,x d >0} pour une classe grande de mouvements brownien subordonnés. Nous montrons que le même test pour l’effilement minimal d’un sous-ensemble sous le graphe d’une fonction non-négative lipschitzienne est valable pour tous les processus dans la classe considérée. Dans le cas classique du mouvement brownien ce test a été démontré par Burdzy.

DOI: 10.5802/aif.2716
Classification: 60J50, 31C40, 31C35, 60J45, 60J75
Keywords: Minimal thinness, subordinate Brownian motion, boundary Harnack principle, Green function, Martin kernel
Mots-clés : effilement minimal, mouvement brownien subordonné, principe de Harnack à la frontiére, fonction de Green, noyau de Martin

Kim, Panki 1; Song, Renming 2; Vondraček, Zoran 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 
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Kim, Panki; Song, Renming; Vondraček, Zoran. Minimal thinness for subordinate Brownian motion in half-space. Annales de l'Institut Fourier, Volume 62 (2012) no. 3, pp. 1045-1080. doi : 10.5802/aif.2716. https://aif.centre-mersenne.org/articles/10.5802/aif.2716/

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