DEL MORAL, Pierre; HORTON, Emma; JASRA, Ajay

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DEL MORAL, Pierre
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]

HORTON, Emma
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]

JASRA, Ajay
King Abdullah University of Science and Technology [Saudi Arabia] [KAUST]

Langue

Article de revue

Ce document a été publié dans

The Annals of Applied Probability. 2022

Institute of Mathematical Statistics (IMS)

Date de soutenance

2022

Résumé en anglais

The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to a class of time-varying positive semigroups. In the context of time-homogeneous models, the regularity conditions discussed in the present article appear to be necessary and sufficient condition for the existence of leading eigenvalues. We review and illustrate the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and signal processing.< Réduire

Mots clés en anglais

Positive semigroups

Boltzmann-Gibbs transformations

Contraction inequalities

Dobrushin's ergodic coefficient

Spectral theorems

Foster-Lyapunov conditions

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190654

Project ANR

Analyse Quantitative de Processus Metastables - ANR-19-CE40-0010

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251