Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators

Farrukh Mukhamedov; Otabek Khakimov; Ahmad Fadillah Embong

doi:10.1007/s12346-020-00415-z

Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators

Farrukh Mukhamedov
, Otabek Khakimov
, Ahmad Fadillah Embong

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (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 ω_V 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 language	English
Article number	79
Journal	Qualitative Theory of Dynamical Systems
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s12346-020-00415-z
Publication status	Published - 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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10.1007/s12346-020-00415-z

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title = "Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators",

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.",

keywords = "Ergodic, Infinite dimensional, Pointwise convergence, Stochastic operator",

author = "Farrukh Mukhamedov and Otabek Khakimov and Embong, \{Ahmad Fadillah\}",

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doi = "10.1007/s12346-020-00415-z",

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T1 - Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators

AU - Mukhamedov, Farrukh

AU - Khakimov, Otabek

AU - Embong, Ahmad Fadillah

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

KW - Ergodic

KW - Infinite dimensional

KW - Pointwise convergence

KW - Stochastic operator

UR - https://www.scopus.com/pages/publications/85089368951

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DO - 10.1007/s12346-020-00415-z

M3 - Article

AN - SCOPUS:85089368951

SN - 1575-5460

VL - 19

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

IS - 3

M1 - 79

ER -

Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators

Abstract

Keywords

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