Boundary Harnack Principle for Subordinate Brownian Motions

Details Boundary Harnack Principle for Subordinate Brownian Motions Boundary Harnack Principle for Subordinate Brownian Motions

2007-08-20

arxiv.org/abs/0708.2583v1

Mathematics

Probability

34 pages

Scientific paper

We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded $\kappa$-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 $\kappa$-fat open sets with respect to these processes with their Euclidean boundary.

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