On convergence rate bounds for a class of nonlinear Markov chains

TL;DR

This paper introduces a novel spectral radius-based approach to evaluate the convergence rates of nonlinear Markov chains, extending linear techniques and applying to extreme value theory.

Contribution

It develops a new method combining spectral radius techniques and perturbation ideas to analyze nonlinear Markov chain convergence rates.

Findings

Provides a new convergence rate bound for nonlinear Markov chains.

Enhances the theoretical understanding of convergence in nonlinear Markov models.

Supports applications in extreme value theory with the new bounds.

Abstract

A new approach is developed for evaluating the convergence rate for nonlinear Markov chains (MC) based on the recently developed spectral radius technique of markovian coupling for linear MC and the idea of small nonlinear perturbations of linear MC. The method further enhances recent advances in the problem of convergence for such models. The new convergence rate may be used, in particular, for the justification of $D$-condition in the Extreme Values theory.