A new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains

2021/10/19 by Aleksandr A. Shchegolev, Shchegolev, Aleksandr A.
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2110.10306

openalex publication_date 2021/10/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition steps. An example of a class such a process provided indicates that such types of estimates considering several transition steps may be applicable when one transition can not guarantee any convergence. Moreover, a better estimate can be obtained for a higher number of transitions steps. A law of large numbers is presented for a class of ergodic nonlinear Markov chains with finite state space that may serve as a basis for nonparametric estimation and other statistics.

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