Potential theory of subordinate Brownian motions with Gaussian components

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Kim, Panki^1,2  Song, Renming³  Vondracek, Zoran⁴ 

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[4] Univ Zagreb, Dept Math, Zagreb 41000, Croatia

关键词: Boundary Harnack principle;    Subordinate Brownian motion;    Harmonic function;    Green function;    Martin boundary;    Levy system;    Exit distribution;   

DOI  :  10.1016/j.spa.2012.11.007

来源: Elsevier

【 摘 要 】

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 Levy 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,C-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,C-1 open set D and identify the Martin boundary of D with respect to the subordinate Brownian motion with the Euclidean boundary. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free