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 Probl. Peredachi Inf., 2007, Volume 43, Issue 4, Pages 51–67 (Mi ppi27)

Large Systems

On Quasi-successful Couplings of Markov Processes

M. L. Blank, S. A. Pirogov

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: The notion of a successful coupling of Markov processes, based on the idea that both components of a coupled system “intersect” in finite time with probability 1, is extended to cover situations where the coupling is not necessarily Markovian and its components only converge (in a certain sense) 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, we consider even more involved situations where the unique ergodicity can be proved only 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.

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English version:
Problems of Information Transmission, 2007, 43:4, 316–330

Bibliographic databases:

UDC: 621.391.1:519.2
Revised: 10.08.2007

Citation: M. L. Blank, S. A. Pirogov, “On Quasi-successful Couplings of Markov Processes”, Probl. Peredachi Inf., 43:4 (2007), 51–67; Problems Inform. Transmission, 43:4 (2007), 316–330

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Blank M., “Metric properties of discrete time exclusion type processes in continuum”, J. Stat. Phys., 140:1 (2010), 170–197
2. Blank M.L., “Unique Ergodicity of a Collective Random Walk”, Dokl. Math., 87:1 (2013), 91–94
3. M. L. Blank, “Interlacing and smoothing: combinatorial aspects”, Problems Inform. Transmission, 50:4 (2014), 350–363
4. Blank M., “Ergodicity of a Collective Random Walk on a Circle”, Nonlinearity, 27:5 (2014), 953–971
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