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 : https://doi.org/10.5802/aif.2716
Classification : 60J50,  31C40,  31C35,  60J45,  60J75
Mots clés : effilement minimal, mouvement brownien subordonné, principe de Harnack à la frontiére, fonction de Green, noyau de Martin
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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://archive.numdam.org/articles/10.5802/aif.2716/

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