On the Stability of Positive Semigroups - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Annals of Applied Probability Year : 2022

On the Stability of Positive Semigroups

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 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.
Fichier principal
Vignette du fichier
positive-sg_arxiv-v6.pdf (531.74 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and 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)

Identifiers

Cite

Pierre del Moral, Emma Horton, Ajay Jasra. On the Stability of Positive Semigroups. Annals of Applied Probability, inPress. ⟨hal-03468416v6⟩
255 View
218 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More