Potential Theory of Subordinate Brownian Motions Revisited

Abstract

The paper discusses and surveys some aspects of the potential theory of subordinate Brownian motion under the assumption that the Laplace exponent of the corresponding subordinator is comparable to a regularly varying function at infinity. This extends some results previously obtained under stronger conditions.

arXiv comment49 pages

Cited by in corpus (7)

• Two-sided Green function estimates for killed subordinate Brownian motions
• Suprema of Lévy processes
• Spectral analysis of subordinate Brownian motions in half-line
• Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes
• First passage times for subordinate Brownian motions
• Minimal thinness for subordinate Brownian motion in half space
• Regularity for fully nonlinear integro-differential operators with regularly varying kernels