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

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)135-153
Number of pages19
JournalPositivity
Volume20
Issue number1
DOIs
Publication statusPublished - Mar 1 2016
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • General Mathematics

Fingerprint

Dive into the research topics of 'Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base'. Together they form a unique fingerprint.

Cite this