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Pré-Publication, Document De Travail Année : 2021

On the Stability of Positive Semigroups

Résumé

The stability and contraction properties of positive integral semigroups on locally compact Polish spaces are investigated. We provide a novel analysis based on an extension of V-norm, Dobrushin-type, contraction techniques on functionally weighted Banach spaces for Markov operators. These are applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. Under mild regularity conditions, the Lipschitz-type contraction analysis presented in this article simplifies and extends several exponential estimates developed in the literature. The spectraltype theorems that we develop can also be seen as an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to time-varying positive semigroups. We review and illustrate in detail the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and advanced signal processing.
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Dates et versions

hal-03468416 , version 1 (07-12-2021)
hal-03468416 , version 2 (03-01-2022)
hal-03468416 , version 3 (10-07-2022)
hal-03468416 , version 4 (16-11-2022)
hal-03468416 , version 5 (16-11-2022)
hal-03468416 , version 6 (17-02-2023)

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Pierre del Moral, Emma Horton, Ajay Jasra. On the Stability of Positive Semigroups. 2021. ⟨hal-03468416v1⟩
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