On the Stability of Positive Semigroups
Language
en
Article de revue
This item was published in
The Annals of Applied Probability. 2022
Institute of Mathematical Statistics (IMS)
Date
2022English Abstract
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 ...Read more >
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.Read less <
English Keywords
Positive semigroups
Boltzmann-Gibbs transformations
Contraction inequalities
Dobrushin's ergodic coefficient
Spectral theorems
Foster-Lyapunov conditions
ANR Project
Analyse Quantitative de Processus Metastables - ANR-19-CE40-0010
Origin
Hal imported