, Volume 17, Issue 1, pp 1-23

Estimates of Green Function for Relativistic α-Stable Process

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Abstract

We call an R d -valued stochastic process X t with characteristic function exp {−t{(m 2/α2)α/2m}},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.