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arXiv · 1909.01237

On the Liouville property for non-local L\'evy generators

Victoria Knopova·René Schilling
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Abstract

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

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Victoria Knopova, René Schilling. 2019-09-03. On the Liouville property for non-local L\'evy generators. https://arxiv.org/abs/1909.01237

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