On mixing in the class of quadratic stochastic operators (Q392468)
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scientific article; zbMATH DE number 6244965
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On mixing in the class of quadratic stochastic operators |
scientific article; zbMATH DE number 6244965 |
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On mixing in the class of quadratic stochastic operators (English)
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14 January 2014
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quadratic stochastic operators
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asymptotic behavior
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nonlinear Markov chains
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nonhomogeneous Markov chains
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mixing nonlinear Markov processes
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This paper is devoted to the quadratic stochastic operators which model the evolution of a biological system. The reader is referred to Yu. J. Lyubich, R. Ganikhodzhaev, F. Mukhamedov and others for historical remarks and an introduction to quadratic stochastic processes.NEWLINENEWLINEThe aim of the paper is to define different types of asymptotic behavior of a quadratic stochastic operator and express them in terms of convergence of a linear nonhomogeneous Markov chain.NEWLINENEWLINESection headings are as follows:NEWLINENEWLINE2. Basics on the ergodic structure of quadratic stochastic operators.NEWLINENEWLINE3. Strong asymptotic stability.NEWLINENEWLINE4. Uniform stability.NEWLINENEWLINE5. Geometric structure of the set of quadratic stochastic operators.
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