Ergodicity of nonlinear Markov operators on the finite dimensional space

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	6769/51167
Uncontrolled Keywords:	Nonlinear Markov operator,Ergodicity,Dobrushin’s ergodicity coefficient, Scrambling stochastic hypermatrix
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Mansoor Saburov
Date Deposited:	27 Jun 2016 12:35
Last Modified:	13 Apr 2017 15:33
URI:	http://irep.iium.edu.my/id/eprint/51167

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