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Markov Chains pp 165-189 | Cite as

Convergence of Atomic Markov Chains

  • Randal DoucEmail author
  • Eric Moulines
  • Pierre Priouret
  • Philippe Soulier
Chapter
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)

Abstract

The main object of this chapter is to prove the convergence of the iterates of a positive recurrent atomic Markov kernel to its invariant probability measure. This will be done by two different methods: application of renewal theory and coupling techniques.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Randal Douc
    • 1
    Email author
  • Eric Moulines
    • 2
  • Pierre Priouret
    • 3
  • Philippe Soulier
    • 4
  1. 1.Département CITITelecom SudParisÉvryFrance
  2. 2.Centre de Mathématiques AppliquéesEcole PloytechniquePalaiseauFrance
  3. 3.Université Pierre et Marie CurieParisFrance
  4. 4.Université Paris NanterreNanterreFrance

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