On the Liouville and strong Liouville properties for a class of non-local operators

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Abstract

We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (the orthogonal subgroup of) the set of zeros of the characteristic exponent of the Lévy process.

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Original languageEnglish
Pages (from-to)365-388
Number of pages24
JournalMathematica Scandinavica
Volume128
Issue number2
Publication statusPublished - 2022
Peer-reviewedYes

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