Green function estimates for relativistic stable processes in half-space-like open sets

Zhen-Qing Chen, Panki Kim and Renming Song

Stochastic Processes and their Applications, 2011, vol. 121, issue 5, 1148-1172

Abstract: In this paper, we establish sharp two-sided estimates for the Green functions of relativistic stable processes (i.e. Green functions for non-local operators m-(m2/[alpha]-[Delta])[alpha]/2) in half-space-like C1,1 open sets. The estimates are uniform in m[set membership, variant](0,M] for each fixed M[set membership, variant](0,[infinity]). When m[downwards arrow]0, our estimates reduce to the sharp Green function estimates for -(-[Delta])[alpha]/2 in such kind of open sets that were obtained recently in Chen and Tokle [12]. As a tool for proving our Green function estimates, we show that a boundary Harnack principle for Xm, which is uniform for all m[set membership, variant](0,[infinity]), holds for a large class of non-smooth open sets.

Keywords: Symmetric; [alpha]-stable; process; Relativistic; stable; process; Green; function; Exit; time; Lévy; system; Uniform; Harnack; inequality; Uniform; boundary; Harnack; principle (search for similar items in EconPapers)
Date: 2011
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