Potential theory of one-dimensional geometric stable processes

• Autorzy: Tomasz Grzywny , Michał Ryznar
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter α ∈ (0,2]. This process has an infinitesimal generator of the form $-log(1+(-Δ)^{α/2})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.

Kategorie tematyczne

• 60J45: Probabilistic potential theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 1
• Strony: 7-40

Daty

wydano

2012

Twórcy

autor

Tomasz Grzywny

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Michał Ryznar

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm129-1-2