Boundary Harnack principle for subordinate Brownian motions

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• 作者：Panki Kim ; Renming Song ; Zoran Vondrač ; ek
• 关键词：Green functions ; Poisson kernels ; Subordinator ; Subordinate Brownian motion ; Bernstein functions ; Complete Bernstein functions ; Symmetric stable processes ; Mixture of symmetric stable processes ; Harmonic functions ; Harnack inequality ; Boundary Harnack pri
• 刊名：Stochastic Processes and their Applications
• 出版年：2009
• 出版时间：May 2009
• 年：2009
• 卷：119
• 期：5
• 页码：1601-1631
• 全文大小：1182 K

文摘

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.