Minimal thinness for subordinate Brownian motion in half-space
[L’effilement minimal pour le mouvement brownien subordonné dans un demi-espace]
Annales de l'Institut Fourier, Tome 62 (2012) no. 3, pp. 1045-1080.

Nous étudions l’effilement minimal dans le demi-espace H:={x=(x ˜,x d ):x ˜ 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.

We study minimal thinness in the half-space H:={x=(x ˜,x d ):x ˜ 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.

DOI : 10.5802/aif.2716
Classification : 60J50, 31C40, 31C35, 60J45, 60J75
Keywords: Minimal thinness, subordinate Brownian motion, boundary Harnack principle, Green function, Martin kernel
Mot 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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     title = {Minimal thinness for subordinate {Brownian} motion in half-space},
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Kim, Panki; Song, Renming; Vondraček, Zoran. Minimal thinness for subordinate Brownian motion in half-space. Annales de l'Institut Fourier, Tome 62 (2012) no. 3, pp. 1045-1080. doi : 10.5802/aif.2716. http://www.numdam.org/articles/10.5802/aif.2716/

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