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On asymptotics for Vaserstein coupling of Markov chains

2013; Elsevier BV; Volume: 123; Issue: 9 Linguagem: Inglês

10.1016/j.spa.2013.04.016

1879-209X

Oleg Butkovsky, A. Yu. Veretennikov,

Graph theory and applications

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a certain "associated" semigroup operator, although, not a "natural" one. We also give sufficient conditions for weak ergodicity and provide explicit estimates of the convergence rate. To establish these results we construct a modification of the Vaserstein coupling. Some applications including mixing properties are also discussed.