Some New Results on Strong Ergodicity

Abstract

Coupling method is used to obtain the explicit upper and lower bounds for convergence rates in strong ergodicity for Markov processes. For one-dimensional diffusion processes and birth-death processes, these bounds are sharp in the sense that the upper one and the lower one are only different by a constant.

Keywords

Markov process / strong ergodicity / coupling / convergence rate / spectral gap

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