Ergodicity of nonlinear Markov operators on the finite dimensional space. (September 2016)

• Record Type: Journal Article
• Authors: Saburov, Mansoor
• Is Part Of: Nonlinear analysis. Volume 143(2016)
• Page Start: 105
• Page End: 119
• Publication Date: 2016-09
• Subjects: 47H25 -- 37A30 -- 47H60; Nonlinear Markov operator -- Ergodicity -- Dobrushin's ergodicity coefficient -- Scrambling stochastic hypermatrix; 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.2016.05.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A nonlinear Markov chain is a discrete time stochastic process whose transition matrices may depend not only on the current state of the process but also on the current distribution of the process. In this paper, we study strong and uniform ergodicity of nonlinear Markov operators defined by stochastic hypermatrices (higher order matrix). We introduce Dobrushin's ergodicity coefficient for a stochastic hypermatrix which enables to study ergodicity of nonlinear Markov operators. By introducing a notion of scrambling stochastic hypermatrix, we study the strong ergodicity of scrambling nonlinear Markov operators.