Boundary Harnack Principle for Subordinate Brownian Motions

2007/08/20 by Kim, Panki, Song, Renming, Vondracek, Zoran
#60J25 #60J45 #60J51 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0708.2583

Abstract

We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded κ-fat open set (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded κ-fat open sets with respect to these processes with their Euclidean boundary.

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