On asymptotics for Vaserstein coupling of Markov chains |
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| Authors: | OA Butkovsky AYu Veretennikov |
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| Institution: | 1. Moscow State University, Faculty of Mathematics and Mechanics, Department of Probability Theory, 119991, Moscow, Russia;2. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK;3. Institute of Information Transmission Problems, Moscow, 127994, Russia |
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| Abstract: | 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. |
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| Keywords: | 60J05 60J22 |
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