Ergodicities of infinite dimensional nonlinear stochastic operators

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 inv...

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Bibliographic Details
Main Authors: Mukhamedov, F., Khakimov, O., Embong, A. F.
Format: Article
Published: Birkhauser 2020
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Online Access:http://eprints.utm.my/id/eprint/93894/
https://doi.org/10.1007/s12346-020-00415-z
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Summary: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.