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Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces

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

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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.

Item Type: Article (Journal)
Additional Information: 5537/29715
Uncontrolled Keywords: Dobrushin ergodicity cofficient; weak ergodic; uniform ergodic; L-1-weak ergodic; von Neumann algebra
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: 23 Apr 2013 14:30
Last Modified: 23 Apr 2013 15:06
URI: http://irep.iium.edu.my/id/eprint/29715

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