Potential theory of subordinate Brownian motions with Gaussian components

Panki Kim, Renming Song and Zoran Vondraček

Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 764-795

Abstract: 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 Lévy 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 C1,1 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 C1,1 open set D and identify the Martin boundary of D with respect to the subordinate Brownian motion with the Euclidean boundary.

Keywords: Boundary Harnack principle; Subordinate Brownian motion; Harmonic function; Green function; Martin boundary; Lévy system; Exit distribution (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spa.2012.11.007

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