ON THE STABILITY OF POSITIVE SEMIGROUPS

• 成果类型: Article
• 署名作者: DEL Moral, Pierre; Horton, Emma; Jasra, Ajay
• 署名单位: Inria; King Abdullah University of Science & Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1923
• 发表日期: 2023
• 页码: 4424-4490
• 关键词: quasi-stationary distributions; uniform particle approximation; fleming-viot processes; feynman-kac formulas; MONTE-CARLO METHODS; nonlinear filters; markov-chains; LIMIT-THEOREMS; stochastic-approximation; exponential stability

摘要

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.