Ergodicity of nonlinear Markov operators on the finite dimensional space
A nonlinear Markov chain is a discrete time stochastic process whose transition matrices may depend not only on the current state of the process but also on the current distribution of the process. In this paper, we study strong and uniform ergodicity of nonlinear Markov operators defined by stocha...
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| Format: | Article |
| Language: | English English English |
| Published: |
Elsevier BV
2016
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| Online Access: | http://irep.iium.edu.my/51167/ http://irep.iium.edu.my/51167/ http://irep.iium.edu.my/51167/ http://irep.iium.edu.my/51167/1/Nonlinear_Markov_Operators_---_NA.pdf http://irep.iium.edu.my/51167/4/51167_Ergodicity%20of%20nonlinear%20Markov_Scopus.pdf http://irep.iium.edu.my/51167/10/51167_Ergodicity%20of%20nonlinear%20Markov_WOS.pdf |
| Summary: | A nonlinear Markov chain is a discrete time stochastic process whose transition matrices may depend not only on the current state of the process but also on the
current distribution of the process. In this paper, we study strong and uniform ergodicity of nonlinear Markov operators defined by stochastic hypermatrices (higher
order matrix). We introduce Dobrushin’s ergodicity coefficient for a stochastic hypermatrix which enables to study ergodicity of nonlinear Markov operators. By
introducing a notion of scrambling stochastic hypermatrix, we study the strong ergodicity of scrambling nonlinear Markov operators. |
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