UNIFORM ERGODICITIES OF MARKOV SEMIGROUPS ON ABSTRACT STATES SPACES

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ERKURŞUN ÖZCAN N., Mukhamedov F.

Journal of Mathematical Sciences (United States), vol.266, no.3, pp.448-460, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 266 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s10958-022-05899-5
  • Journal Name: Journal of Mathematical Sciences (United States)
  • Journal Indexes: Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.448-460
  • Keywords: C-Markov semigroup, Ergodicity coefficient, Perturbation bound, Uniform P-ergodicity
  • Hacettepe University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.The present paper is devoted to the investigation of uniform stabilities of positive C-semigroups defined on abstract state spaces by means of a generalized Dobrushin ergodicity coefficient. The most known results in the literature were obtained for Markov semigroups acting on Banach lattices having unique invariant states. The essence of the present paper is that the considered Markov semigroups (acting on abstract state spaces) do not generally have invariant states and, moreover, abstract state spaces need not necessarily be lattices, implying that the results of the paper are principal in this direction.