Abstract
We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in κ-fat open sets (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 boundaries.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1601-1631 |
| Number of pages | 31 |
| Journal | Stochastic Processes and their Applications |
| Volume | 119 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2009 |
Keywords
- Bernstein functions
- Boundary Harnack principle
- Complete Bernstein functions
- Green functions
- Harmonic functions
- Harnack inequality
- Martin boundary
- Mixture of symmetric stable processes
- Poisson kernels
- Subordinate Brownian motion
- Subordinator
- Symmetric stable processes
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics