On Convergence Rate Bounds for a Class of Nonlinear Markov Chains

A.A. Shchegolev, A.Yu. Veretennikov

2023, v.29, Issue 5, 619-639


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.


Keywords: nonlinear Markov chains; uniform ergodicity; convergence rate; Marko- vian coupling; spectral radius, extreme values


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