Recurrence and Ergodicity

  • Pierre Brémaud
Part of the Texts in Applied Mathematics book series (TAM, volume 31)


Consider a Markov chain taking its values in E = ℕ. There is a possibility that for any initial state i ∈ ℕ the chain will never visit i after some finite random time. This is often an undesirable feature. For example, if the chain counts the number of customers waiting in line at a service counter (we shall see Markovian models of waiting lines, or queues, at different places in this book), such a behavior implies that the waiting line will eventually go beyond the limits of the waiting facility. In a sense, the corresponding system is unstable.


Markov Chain Stationary Distribution Invariant Measure Transition Matrix Ergodic Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Pierre Brémaud
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS-ESEGif-sur-YvetteFrance

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