Markov Chains pp 125-165 | Cite as

Long Run Behavior

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


Consider an HMC that is irreducible and positive recurrent. In particular, if its initial distribution is the stationary distribution, it keeps the same distribution at all times. The chain is then said to be in the stationary regime, or in equilibrium, or in steady state.


Transition Matrix Transient State Fundamental Matrix Renewal Time Renewal Equation 


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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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