On mixing in the class of quadratic stochastic operators

Wojciech Bartoszek; Małgorzata Pułka

doi:10.1016/j.na.2013.03.011

On mixing in the class of quadratic stochastic operators

Abstract

We study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic stochastic operator is prevalent.

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS no. 86, pages 95 - 113,
ISSN: 0362-546X
Language:: English
Publication year:: 2013
Bibliographic description:: Bartoszek W., Pułka M.: On mixing in the class of quadratic stochastic operators// NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. -Vol. 86, (2013), s.95-113
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.na.2013.03.011
Verified by:: Gdańsk University of Technology