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

被引：0
作者：
Farrukh Mukhamedov
机构：
[1] International Islamic University Malaysia,Department of Computational and Theoretical Sciences, Faculty of Science
来源：
Positivity | 2016年 / 20卷
关键词：
Coefficient of ergodicity; Strong ergodicity; Weak ergodicity; Nonhomogeneous Markov chain; Norm ordered space; 47A35; 28D05;
D O I：
暂无
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摘要：
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.
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页码：135 / 153
页数：18
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