Cover Image

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Mukhamedov, F., Khakimov, O., Embong, A. F.
Format: Article
Published: Birkhauser 2020
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/93894/
https://doi.org/10.1007/s12346-020-00415-z
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.utm.93894
record_format eprints
spelling 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
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle 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 13.250246

Similar Items