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The (strong) Liouville property for a class of non-local operators

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David Berger, René L. Schilling

Probability · Submitted 5 Jan 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a L\'evy process and subordinate L\'evy processes.

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arXiv ID2101.01592 (version 3)
Pith IDYELUCLLJ, Pith's permanent record of this paper and its review
CitationDavid Berger, Ren\'e L. Schilling. "The (strong) Liouville property for a class of non-local operators." arXiv:2101.01592 (2021). https://pith.science/paper/YELUCLLJ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,343 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We prove a necessary and sufficient condition for the Liouville and strong Liouville properties 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 set of zeros of the characteristic exponent of the L\'evy process.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a L\'evy process and subordinate L\'evy processes. result 0.56 0.96 0.87 asserted 1.00
s1 Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (orthogonal subgroup of) the set of zeros of the characteristic exponent of the L\'evy process. result 0.85 0.87 0.20 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove a necessary and sufficient condition for the Liouville and strong Liouville properties 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 set of zeros of the characteristic exponent of the L\'evy process.

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1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Compares with 1 paper
  • Our results complement previous work by Kühn [ref] who looks at not necessarily positive solutions $f$ which have polynomial growth.

    A Liouville theorem for L\'evy generators · Towards the strong Liouville property · 0.89

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