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On quasi-successful couplings of Markov processes. (English. Russian original) Zbl 1156.60055
Probl. Inf. Transm. 43, No. 4, 316-330 (2007); translation from Probl. Peredachi Inf. 43, No. 4, 51-67 (2007).
Authors’ summary slightly altered. “The notion of a successful coupling of Markov processes is based on the idea that the components of a coupled system ‘intersect’ in finite time with probability \(1\). This idea is extended to cover situations where the coupling is not necessarily Markovian and its components only get arbitrarily close to each other with time. Under these assumptions, the unique ergodicity of the original Markov process is proved. The price for this generalization is the weak convergence to the unique invariant measure instead of the strong convergence. Applying these ideas to infinite interacting particle systems, the authors consider even more involved situations where the unique ergodicity can be only proved for a restriction of the original system to a certain class of initial distributions (e.g., translation-invariant). Questions about the existence of invariant measures with a given particle density are also discussed.”

MSC:
60J05 Discrete-time Markov processes on general state spaces
60K99 Special processes
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