On an irreducibility type condition for the ergodicity of nonconservative semigroups
We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semigroups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of ir...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2020-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.92/ |
| _version_ | 1797651550531747840 |
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| author | Cloez, Bertrand Gabriel, Pierre |
| author_facet | Cloez, Bertrand Gabriel, Pierre |
| author_sort | Cloez, Bertrand |
| collection | DOAJ |
| description | We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semigroups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment. |
| first_indexed | 2024-03-11T16:17:26Z |
| format | Article |
| id | doaj.art-90ca90916d63488aa6590240090e9f35 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:26Z |
| publishDate | 2020-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-90ca90916d63488aa6590240090e9f352023-10-24T14:18:57ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-10-01358673374210.5802/crmath.9210.5802/crmath.92On an irreducibility type condition for the ergodicity of nonconservative semigroupsCloez, Bertrand0Gabriel, Pierre1MISTEA, INRAE, Montpellier SupAgro, Univ. Montpellier, 2 place Pierre Viala, 34060 Montpellier, FranceLaboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 45 Avenue des États-Unis, 78035 Versailles cedex, FranceWe propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semigroups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.92/ |
| spellingShingle | Cloez, Bertrand Gabriel, Pierre On an irreducibility type condition for the ergodicity of nonconservative semigroups Comptes Rendus. Mathématique |
| title | On an irreducibility type condition for the ergodicity of nonconservative semigroups |
| title_full | On an irreducibility type condition for the ergodicity of nonconservative semigroups |
| title_fullStr | On an irreducibility type condition for the ergodicity of nonconservative semigroups |
| title_full_unstemmed | On an irreducibility type condition for the ergodicity of nonconservative semigroups |
| title_short | On an irreducibility type condition for the ergodicity of nonconservative semigroups |
| title_sort | on an irreducibility type condition for the ergodicity of nonconservative semigroups |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.92/ |
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