On non-ergodic volterra cubic stochastic operators
Let Sm−1 be the simplex in Rm , and V:Sm−1→Sm−1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit limn→∞1n∑k=1nVk(x) exists for every x∈Sm−1 . It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to char...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Springer
2019
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/8/73972%20On%20Non-ergodic%20Volterra%20Cubic%20-In-press.pdf http://irep.iium.edu.my/73972/9/73972%20On%20Non-ergodic%20Volterra%20Cubic%20-In-press%20SCOPUS%20pdf.pdf |
| Summary: | Let Sm−1 be the simplex in Rm , and V:Sm−1→Sm−1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit
limn→∞1n∑k=1nVk(x) exists for every x∈Sm−1 . It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to characterize all non-ergodic operators. However, there is an ongoing problem even in the low dimensional simplexes. In this paper, we solve the mentioned problem within Volterra cubic stochastic operators acting on two-dimensional simplex. |
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