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Positivity

, Volume 20, Issue 1, pp 135–153 | Cite as

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

  • Farrukh MukhamedovEmail author
Article

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.

Keywords

Coefficient of ergodicity Strong ergodicity Weak ergodicity Nonhomogeneous Markov chain Norm ordered space 

Mathematics Subject Classification

47A35 28D05 

Notes

Acknowledgments

The author acknowledges the MOE grant FRGS14-135-0376 and the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Computational and Theoretical Sciences, Faculty of ScienceInternational Islamic University MalaysiaKuantanMalaysia

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