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On the central limit theorem for homogeneous discrete-time nonlinear Markov chains

Aleksandr Shchegolev
Dec 2022
摘要
The class of nonlinear Markov processes is characterized by the dependence ofthe current state of the process on its current distribution in addition to thedependence on the previous state. Due to this feature, these processes arecharacterized by complex limit behavior and ergodic properties, for which theusual criteria for Markov processes are not sufficient. Being a subclass ofnonlinear Markov processes, nonlinear Markov chains have inherited thesefeatures. In this paper, conditions for the fulfillment of the central limittheorem for homogeneous nonlinear Markov chains in discrete time and with adiscrete finite state space are studied. Also, a brief review of known resultson the ergodic properties of nonlinear Markov chains is included. The obtainedresult complements the existing results in this area and may be useful forfurther applications in statistics.
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