Potential theory of subordinate Brownian motions with Gaussian components (CROSBI ID 187635)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Kim, Panki ; Song, Renming ; Vondraček, Zoran
engleski
Potential theory of subordinate Brownian motions with Gaussian components
In this paper we study a subordinate Brownian motion with a Gaussian component and a rather general discontinuous part. The assumption on the subordinator is that its Laplace exponent is a complete Bernstein function with a L\'evy density satisfying a certain growth condition near zero. The main result is a boundary Harnack principle with explicit boundary decay rate for non-negative harmonic functions of the process in $C^{; ; ; ; 1, 1}; ; ; ; $ open sets. As a consequence of the boundary Harnack principle, we establish sharp two-sided estimates on the Green function of the subordinate Brownian motion in any bounded $C{; ; ; ; 1, 1}; ; ; ; $ open set $D$ and identify the Martin boundary of $D$ with respect to the subordinate Brownian motion with the Euclidean boundary.
boundary Harnack principle ; subordinate Brownian motion ; harmonic function ; Green function ; Martin boundary ; Levy system ; exit distribution
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Podaci o izdanju
123 (3)
2013.
764-795
objavljeno
0304-4149
1879-209X
10.1016/j.spa.2012.11.007