On Harnack Inequality and Hölder Regularity for Isotropic Unimodal Lévy Processes
By T. Grzywny. 2013
106 citations recorded by the source corpus.
We prove the scale invariant Harnack inequality and regularity properties for harmonic functions with respect to an isotropic unimodal Lévy process with the characteristic exponent ψ satisfying some scaling condition. We derive sharp estimates of the potential measure and capacity of balls, and further, under the assumption that ψ satisfies the lower scaling condition, sharp estimates of the potential kernel of the underlying process. This allows us to establish the Krylov–Safonov type estimate, which is the key ingredient in the approach of Bass and Levin, that we follow.
Subfields: Applied Mathematics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/5eba4a8ae7230b6037716ecc053bf83cad4e057f
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In Applied Mathematics
- Tadeusz Kulczycki
- M. Ryznar
- Krzysztof Bogdan
- Tomasz Jakubowski
- Renming Song
- Mateusz Kwaśnicki
- Bartłlomiej Dyda
- Zhen-Qing Chen
In Finance
- Tadeusz Kulczycki
- M. Ryznar
- Renming Song
- Krzysztof Bogdan
- Mateusz Kwaśnicki
- Bartłlomiej Dyda
- Tomasz Jakubowski
- Zhen-Qing Chen
In Management Science and Operations Research
Citations in the corpus
- Gradient estimates of harmonic functions and transition densities for Levy processes (2013, background): “Grzywny in [14] obtained estimates of the potential kernel in terms of the symbol ψ, which play an important role in the present paper.”