Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators

Farrukh Mukhamedov, Otabek Khakimov, Ahmad Fadillah Embong

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In the present paper, we introduce two classes L+ and L- of nonlinear stochastic operators acting on the simplex of ℓ1-space. For each operator V from these classes, we study omega limiting sets ωV and ωV(w) with respect to ℓ1-norm and pointwise convergence, respectively. As a consequence of the investigation, we establish that every operator from the introduced classes is weak ergodic. However, if V belongs to L-, then it is not ergodic (w.r.t ℓ1-norm) while V is weak ergodic.

Original languageEnglish
Article number79
JournalQualitative Theory of Dynamical Systems
Volume19
Issue number3
DOIs
Publication statusPublished - Dec 1 2020

Keywords

  • Ergodic
  • Infinite dimensional
  • Pointwise convergence
  • Stochastic operator

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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