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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Birkhauser
2020
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my.utm.938942022-02-28T13:12:21Z http://eprints.utm.my/id/eprint/93894/ Ergodicities of infinite dimensional nonlinear stochastic operators Mukhamedov, F. Khakimov, O. Embong, A. F. QA Mathematics 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. Birkhauser 2020 Article PeerReviewed Mukhamedov, F. and Khakimov, O. and Embong, A. F. (2020) Ergodicities of infinite dimensional nonlinear stochastic operators. Qualitative Theory of Dynamical Systems, 19 (3). ISSN 1575-5460 https://doi.org/10.1007/s12346-020-00415-z DOI: 10.1007/s12346-020-00415-z |
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QA Mathematics Mukhamedov, F. Khakimov, O. Embong, A. F. Ergodicities of infinite dimensional nonlinear stochastic operators |
| description |
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. |
| format |
Article |
| author |
Mukhamedov, F. Khakimov, O. Embong, A. F. |
| author_facet |
Mukhamedov, F. Khakimov, O. Embong, A. F. |
| author_sort |
Mukhamedov, F. |
| title |
Ergodicities of infinite dimensional nonlinear stochastic operators |
| title_short |
Ergodicities of infinite dimensional nonlinear stochastic operators |
| title_full |
Ergodicities of infinite dimensional nonlinear stochastic operators |
| title_fullStr |
Ergodicities of infinite dimensional nonlinear stochastic operators |
| title_full_unstemmed |
Ergodicities of infinite dimensional nonlinear stochastic operators |
| title_sort |
ergodicities of infinite dimensional nonlinear stochastic operators |
| publisher |
Birkhauser |
| publishDate |
2020 |
| url |
http://eprints.utm.my/id/eprint/93894/ https://doi.org/10.1007/s12346-020-00415-z |
| _version_ |
1726791450363953152 |
| score |
13.251813 |