Asymptotic properties of quadratic stochastic operators acting on the L1 space. (February 2015)

• Record Type: Journal Article
• Authors: Bartoszek, Krzysztof; Pułka, Małgorzata
• Is Part Of: Nonlinear analysis. Volume 114(2015)
• Page Start: 26
• Page End: 39
• Publication Date: 2015-02
• Subjects: 47A35 -- 47B65 -- 47B07 -- 92B99; Quadratic stochastic operators -- Nonhomogeneous Markov operators -- Mixing nonlinear Markov process; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.10.032
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ 1 space. It turns out that in principle most of the results can be carried over to the L 1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L 1 space in terms of convergence of the associated (linear) nonhomogeneous Markov chains.