Markov Chains pp 241-264 | Cite as

Splitting Construction and Invariant Measures

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


Chapter  6 was devoted to the study of Markov kernels admitting an accessible atom. The existence of an accessible atom had very important consequences, in particular for the existence and characterization of invariant measures. These results cannot be used if the state space does not admit an atom, which is the most frequent case for Markov kernels on a general state space.

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© 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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