Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base

Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base

It is known that the Dobrushin’s ergodicity coefficient is one of the effective tools to study the behavior of non-homogeneous Markov chains. In the present paper, we define such an ergodicity coefficient of a positive mapping defined on ordered Banach spaces with a base (OBSB), and study its proper...

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Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
Published: Springer 2015
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/46020/
http://irep.iium.edu.my/46020/
http://irep.iium.edu.my/46020/
http://irep.iium.edu.my/46020/1/46020.pdf
id iium-46020
recordtype eprints
spelling iium-460202017-08-08T07:26:41Z http://irep.iium.edu.my/46020/ Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base Mukhamedov, Farrukh QA Mathematics It is known that the Dobrushin’s ergodicity coefficient is one of the effective tools to study the behavior of non-homogeneous Markov chains. In the present paper, we define such an ergodicity coefficient of a positive mapping defined on ordered Banach spaces with a base (OBSB), and study its properties. In terms of this coefficient we prove the equivalence uniform and weak ergodicities of homogeneous Markov chains. This extends earlier results obtained in case of von Neumann algebras. Such a result allows to establish a category theorem for uniformly ergodic Markov operators. We find necessary and sufficient conditions for the weak ergodicity of nonhomogeneous discrete Markov chains (NDMC). L-weak ergodicity of NDMC defined on OBSB is also studied. We establish that the chain satisfies L-weak ergodicity if and only if it satisfies a modified Doeblin’s condition (D1 -condition). Moreover, some connections between L-weak ergodicity and L-strong ergodicity have been established. Several nontrivial examples of NDMC which satisfy the D1-condition are provided. Springer 2015-09-22 Article PeerReviewed application/pdf en http://irep.iium.edu.my/46020/1/46020.pdf Mukhamedov, Farrukh (2015) Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base. Acta Mathematica Hungarica, 147 (2). pp. 294-323. ISSN 1588-2632 (O), 0236-5294 (P) E-ISSN 1588-2632 http://link.springer.com/article/10.1007%2Fs10474-015-0545-2#page-1 10.1007/s10474-015-0545-2
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
description It is known that the Dobrushin’s ergodicity coefficient is one of the effective tools to study the behavior of non-homogeneous Markov chains. In the present paper, we define such an ergodicity coefficient of a positive mapping defined on ordered Banach spaces with a base (OBSB), and study its properties. In terms of this coefficient we prove the equivalence uniform and weak ergodicities of homogeneous Markov chains. This extends earlier results obtained in case of von Neumann algebras. Such a result allows to establish a category theorem for uniformly ergodic Markov operators. We find necessary and sufficient conditions for the weak ergodicity of nonhomogeneous discrete Markov chains (NDMC). L-weak ergodicity of NDMC defined on OBSB is also studied. We establish that the chain satisfies L-weak ergodicity if and only if it satisfies a modified Doeblin’s condition (D1 -condition). Moreover, some connections between L-weak ergodicity and L-strong ergodicity have been established. Several nontrivial examples of NDMC which satisfy the D1-condition are provided.
format Article
author Mukhamedov, Farrukh
author_facet Mukhamedov, Farrukh
author_sort Mukhamedov, Farrukh
title Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_short Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_full Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_fullStr Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_full_unstemmed Ergodic properties of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_sort ergodic properties of nonhomogeneous markov chains defined on ordered banach spaces with a base
publisher Springer
publishDate 2015
url http://irep.iium.edu.my/46020/
http://irep.iium.edu.my/46020/
http://irep.iium.edu.my/46020/
http://irep.iium.edu.my/46020/1/46020.pdf
first_indexed 2023-09-18T21:05:29Z
last_indexed 2023-09-18T21:05:29Z
_version_ 1777410904667717632

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