Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces

In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned on noncommutative L 1 -spaces associated with semi-�nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to i...

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Main Author:	Mukhamedov, Farrukh
Format:	Article
Language:	English
Published:	Ferdowsi University of Mashhad. 2013
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/29715/ http://irep.iium.edu.my/29715/ http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf

id	iium-29715
recordtype	eprints
spelling	iium-297152013-04-23T07:06:01Z http://irep.iium.edu.my/29715/ Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces Mukhamedov, Farrukh QA Mathematics In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned on noncommutative L 1 -spaces associated with semi-�nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to in- vestigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coe�cient. We provide a su�cient condi- tions for such processes to satisfy the weak ergodicity. Moreover, a necessary and su�cient condition is given for the satisfaction of the L 1 -weak ergodicity of NDMP. It is also provided an example showing that L 1 -weak ergodicity is weaker that weak ergodicity. We applied the main results to several concrete examples of noncommutative NDMP. Ferdowsi University of Mashhad. 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf Mukhamedov, Farrukh (2013) Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces. Banach Journal of Mathematical Analysis, 7 (2). pp. 53-73. ISSN 1735-8787 http://www.emis.de/journals/BJMA/
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 Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
description	In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned on noncommutative L 1 -spaces associated with semi-�nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to in- vestigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coe�cient. We provide a su�cient condi- tions for such processes to satisfy the weak ergodicity. Moreover, a necessary and su�cient condition is given for the satisfaction of the L 1 -weak ergodicity of NDMP. It is also provided an example showing that L 1 -weak ergodicity is weaker that weak ergodicity. We applied the main results to several concrete examples of noncommutative NDMP.
format	Article
author	Mukhamedov, Farrukh
author_facet	Mukhamedov, Farrukh
author_sort	Mukhamedov, Farrukh
title	Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
title_short	Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
title_full	Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
title_fullStr	Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
title_full_unstemmed	Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
title_sort	weak ergodicity of nonhomogeneous markov chains on noncommutative l1-spaces
publisher	Ferdowsi University of Mashhad.
publishDate	2013
url	http://irep.iium.edu.my/29715/ http://irep.iium.edu.my/29715/ http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf
first_indexed	2023-09-18T20:43:40Z
last_indexed	2023-09-18T20:43:40Z
_version_	1777409531829026816

Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces

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