Name: A Liouville theorem for Lévy generators
Creator: Franziska Kühn
Keywords: 60G51, 35B53, 31C05, 35R09, 60J35, Mathematics - Analysis of PDEs, Probability (math.PR), FOS: Mathematics, 0101 mathematics, 16. Peace & justice, 01 natural sciences, Mathematics - Probability, Analysis of PDEs (math.AP), 12. Responsible consumption

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 08 Dec 2020Embargo end date: 01 Jan 2020 English Publisher:Springer Science and Business Media LLCJournal:Positivity, volume 25, pages 997-1,012 (issn: 1385-1292, eissn: 1572-9281,

Authors: Franziska Kühn;

doi: 10.1007/s11117-020-00800-7 , 10.48550/arxiv.2001.02528

arXiv: http://arxiv.org/abs/2001.02528

A Liouville theorem for Lévy generators

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Abstract

AbstractUnder mild assumptions, we establish a Liouville theorem for the “Laplace” equation $$Au=0$$ A u = 0 associated with the infinitesimal generator A of a Lévy process: If u is a weak solution to $$Au=0$$ A u = 0 which is at most of (suitable) polynomial growth, then u is a polynomial. As a by-product, we obtain new regularity estimates for semigroups associated with Lévy processes.

Related Organizations

TU Dresden
Germany
TU Dresden
Germany
TU Dresden
Germany

Keywords

60G51, 35B53, 31C05, 35R09, 60J35, Mathematics - Analysis of PDEs, Probability (math.PR), FOS: Mathematics, Mathematics - Probability, Analysis of PDEs (math.AP)

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