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Geometric Ergodicity

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

Abstract

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.

Keywords

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