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arXiv · 2209.12834

On convergence rate bounds for a class of nonlinear Markov chains

Alexander Shchegolev·Alexander Veretennikov
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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.

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Alexander Shchegolev, Alexander Veretennikov. 2022-09-26. On convergence rate bounds for a class of nonlinear Markov chains. https://doi.org/10.61102/1024-2953-mprf.2023.29.5.001

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