TY - JOUR
T1 - Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators
AU - Mukhamedov, Farrukh
AU - Khakimov, Otabek
AU - Embong, Ahmad Fadillah
N1 - Funding Information:
The present work is supported by the UAEU UPAR Grant No. 31S391.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
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
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U2 - 10.1007/s12346-020-00415-z
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 -