A new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains
Probability
2021-10-22 v1
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.
Keywords
Cite
@article{arxiv.2110.10306,
title = {A new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains},
author = {Aleksandr A. Shchegolev},
journal= {arXiv preprint arXiv:2110.10306},
year = {2021}
}