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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2016
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my.iium.irep.511672017-04-13T07:33:56Z http://irep.iium.edu.my/51167/ Ergodicity of nonlinear Markov operators on the finite dimensional space Saburov, Mansoor QA Mathematics 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. Elsevier BV 2016-09 Article REM application/pdf en http://irep.iium.edu.my/51167/1/Nonlinear_Markov_Operators_---_NA.pdf application/pdf en http://irep.iium.edu.my/51167/4/51167_Ergodicity%20of%20nonlinear%20Markov_Scopus.pdf application/pdf en http://irep.iium.edu.my/51167/10/51167_Ergodicity%20of%20nonlinear%20Markov_WOS.pdf Saburov, Mansoor (2016) Ergodicity of nonlinear Markov operators on the finite dimensional space. Nonlinear Analysis: Theory, Methods and Applications, 143. pp. 105-119. ISSN 0362-546X (In Press) http://www.sciencedirect.com/science/article/pii/S0362546X16300712 10.1016/j.na.2016.05.006 |
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QA Mathematics Saburov, Mansoor Ergodicity of nonlinear Markov operators on the finite dimensional space |
| description |
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. |
| format |
Article |
| author |
Saburov, Mansoor |
| author_facet |
Saburov, Mansoor |
| author_sort |
Saburov, Mansoor |
| title |
Ergodicity of nonlinear Markov operators on the finite
dimensional space |
| title_short |
Ergodicity of nonlinear Markov operators on the finite
dimensional space |
| title_full |
Ergodicity of nonlinear Markov operators on the finite
dimensional space |
| title_fullStr |
Ergodicity of nonlinear Markov operators on the finite
dimensional space |
| title_full_unstemmed |
Ergodicity of nonlinear Markov operators on the finite
dimensional space |
| title_sort |
ergodicity of nonlinear markov operators on the finite
dimensional space |
| publisher |
Elsevier BV |
| publishDate |
2016 |
| url |
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 http://irep.iium.edu.my/51167/ http://www.sciencedirect.com/science/article/pii/S0362546X16300712 |
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