Naslov
Minimal thinness for subordinate Brownian motion in half-space

Autori
Kim, Panki ; Song, Renming ; Vondraček, Zoran

Izvornik
Annales de l institut fourier (0373-0956) 62 (2012), 3; 1045-1080

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
minimal thinness ; subordinate Brownian motion ; boundary Harnack principle ; Green function ; Martin kernel

Sažetak
We study minimal thinness in the half-space $H:=\ {; ; ; ; ; ; ; x=(\wt{; ; ; ; ; ; ; x}; ; ; ; ; ; ; , x_d):\, \wt{; ; ; ; ; ; ; x}; ; ; ; ; ; ; \in \R^{; ; ; ; ; ; ; d-1}; ; ; ; ; ; ; , x_d>0\}; ; ; ; ; ; ; $ for a large class of rotationally invariant L\'evy processes, including symmetric stable processes and sums of Brownian motion and independent stable processes. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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