Geometric Ergodicity

  • Sean P. Meyn
  • Richard L. Tweedie
Part of the Communications and Control Engineering Series book series (CCE)


The previous two chapters have shown that for positive Harris chains, convergence of Ex[ƒ(Φk)] is guaranteed from almost all initial states x provided only π(ƒ) < ∞. Strong though this is, for many models used in practice even more can be said: there is often a rate of convergence ρ such that
$$||{P^n}\left( {x,\cdot} \right) - \pi |{|_f} = o\left( {{\rho ^n}} \right)$$
where the rate ρ < 1 can be chosen essentially independent of the initial point x.


Invariant Probability Measure Simple Random Walk Simple Linear Model Strong Markov Property Countable Space 
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Copyright information

© Springer-Verlag London Limited 1993

Authors and Affiliations

  • Sean P. Meyn
    • 1
  • Richard L. Tweedie
    • 2
  1. 1.Coordinated Science Laboratory and the Department of Electrical and Computer EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Department of StatisticsColorado State UniversityFort CollinsUSA

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