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Markov Chains pp 195-251 | Cite as

Eigenvalues and Nonhomogeneous Markov Chains

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

Abstract

When the state space is finite, we can rely on the standard results of linear algebra to study the asymptotic behavior of homogeneous Markov chains. Indeed, the asymptotic behavior of the distribution at time n of the chain is entirely described by the asymptotic behavior of the n-step transition matrix P n and the latter depends on the eigenstructure of P. The Perron-Frobenius theorem detailing the eigenstructure of nonnegative matrices is therefore all that is needed, at least in the theory.

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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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