Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions (CROSBI ID 195596)
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Kim, Panki ; Song, Renming ; Vondraček, Zoran
engleski
Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions
In this paper we study the Martin boundary of unbounded open sets at infinity for a large class of subordinate Brownian motions. We first prove that, for such subordinate Brownian motions, the uniform boundary Harnack principle at infinity holds for arbitrary unbounded open sets. Then we introduce the notion of $\kappa$-fatness at infinity for open sets and show that the Martin boundary at infinity of any such open set consists of exactly one point and that point is a minimal Martin boundary point.
Levy processes ; subordinate Brownian motion ; harmonic functions ; boundary Harnack principle ; Martin kernel ; Martin boundary ; Poisson kernel
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