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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| Main Authors: | , , |
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| Format: | Article |
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Birkhauser
2020
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| Subjects: | |
| 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. |
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