Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base

Mukhamedov, Farrukh (2016) Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base. Positivity, 20 (1). pp. 135-153. ISSN 1385-1292 E-ISSN 1572-9281

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Abstract

In the present paper, we define an ergodicity coefficient of a positive mapping defined on ordered Banach space with a base , and study its properties. The defined coefficient is a generalization of the well-known the Dobrushin’s ergodicity coefficient. By means of the ergodicity coefficient we provide uniform asymptotical stability conditions for nonhomogeneous discrete Markov chains (NDMC). These results are even new in case of von Neumann algebras. Moreover, we find necessary and sufficient conditions for the weak ergodicity of NDMC. Certain relations between uniform asymptotical stability and weak ergodicity are considered.

Item Type:	Article (Journal)
Additional Information:	5537/49815
Uncontrolled Keywords:	Coefficient of ergodicity, Strong ergodicity, Weak ergodicity, Nonhomogeneous Markov chain, Norm ordered space
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	06 Apr 2016 10:35
Last Modified:	05 Apr 2017 15:19
URI:	http://irep.iium.edu.my/id/eprint/49815

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