Abstract
We call an R d-valued stochastic process X t with characteristic function exp {−t{(m 2/α+ξ2)α/2−m}},ξ∈R d,m>0, the relativistic α-stable process. In the paper we derive sharp estimates for the Green function of the relativistic α-stable process on C 1,1 domains. Using these estimates we provide lower and upper bounds for the Poisson kernel. As another application we derive 3G Theorem and Boundary Harnack Principle for C 1,1 domains.
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Ryznar, M. Estimates of Green Function for Relativistic α-Stable Process. Potential Analysis 17, 1–23 (2002). https://doi.org/10.1023/A:1015231913916
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DOI: https://doi.org/10.1023/A:1015231913916