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, Malezya, 22 - 26 Ağustos 2016, cilt.819, (Tam Metin Bildiri) identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 819
  • Doi Numarası: 10.1088/1742-6596/819/1/012015
  • Basıldığı Şehir: Kuantan
  • Basıldığı Ülke: Malezya
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.