Potential Analysis

, Volume 17, Issue 1, pp 1–23 | Cite as

Estimates of Green Function for Relativistic α-Stable Process

  • MichaŁ Ryznar
Article

Abstract

We call an R d -valued stochastic process X t with characteristic function exp {−t{(m2/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 C1,1 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 C1,1 domains.

stable and relativistic stable processes Green function harmonic functions Poisson kernel 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • MichaŁ Ryznar
    • 1
  1. 1.Institute of MathematicsWroclaw University of TechnologyWrocławPoland

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