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Markov Chains pp 221-239 | Cite as

Transience, Recurrence, and Harris Recurrence

  • 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

Recurrence and transience properties have already been examined in Chapter  6 and  7 for atomic and discrete Markov chains. We revisit these notions for irreducible Markov chains. Some of the properties we have shown for atomic chains extend quite naturally to irreducible chains. This is in particular true of the dichotomy between recurrent and transient chains (compare Theorem  6.2.7 or Theorem  7.1.2 with Theorem 10.1.5 below).

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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