Boundary potential theory for stable Lévy processes

• Autorzy: Paweł Sztonyk
• Języki publikacji: EN

Abstrakty

EN

We investigate properties of harmonic functions of the symmetric stable Lévy process on $ℝ^{d}$ without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for such functions.

Kategorie tematyczne

• 60J45: Probabilistic potential theory
• 60G51: Processes with independent increments; L\'evy processes
• 31C05: Harmonic, subharmonic, superharmonic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 95
• Numer: 2
• Strony: 191-206

Daty

wydano

2003

Twórcy

autor

Paweł Sztonyk

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

Identyfikatory

DOI

10.4064/cm95-2-4