We study minimal thinness in the half-space for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of 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 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.
Revised:
Accepted:
DOI: 10.5802/aif.2716
Classification: 60J50, 31C40, 31C35, 60J45, 60J75
Keywords: Minimal thinness, subordinate Brownian motion, boundary Harnack principle, Green function, Martin kernel
@article{AIF_2012__62_3_1045_0, author = {Kim, Panki and Song, Renming and Vondra\v{c}ek, Zoran}, title = {Minimal thinness for subordinate {Brownian} motion in half-space}, journal = {Annales de l'Institut Fourier}, pages = {1045--1080}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {3}, year = {2012}, doi = {10.5802/aif.2716}, zbl = {1273.60096}, mrnumber = {3013816}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2716/} }
TY - JOUR TI - Minimal thinness for subordinate Brownian motion in half-space JO - Annales de l'Institut Fourier PY - 2012 DA - 2012/// SP - 1045 EP - 1080 VL - 62 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2716/ UR - https://zbmath.org/?q=an%3A1273.60096 UR - https://www.ams.org/mathscinet-getitem?mr=3013816 UR - https://doi.org/10.5802/aif.2716 DO - 10.5802/aif.2716 LA - en ID - AIF_2012__62_3_1045_0 ER -
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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