Uniform ergodicities and perturbation bounds of Markov chains on ordered Banach spaces

Ozcan N., Mukhamedov F.

37th International Conference on Quantum Probability and Related Topics (QP), Kuantan, Malaysia, 22 - 26 August 2016, vol.819 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 819
  • Doi Number: 10.1088/1742-6596/819/1/012015
  • City: Kuantan
  • Country: Malaysia
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we consider uniformly mean ergodic and uniformly asymptotical stable Markov operators on ordered Banach spaces. In terms of the ergodicity coefficient, we show the equivalence of uniform and weak mean ergodicities of Markov operators. This result allowed us to establish a category theorem for uniformly mean ergodic Markov operators. Furthermore, using properties of the ergodicity coefficient, we develop the perturbation theory for uniformly asymptotical stable Markov chains in the abstract scheme.