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Continuous dependence of ergodic limits

Author

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  • Goldstein, Jerome A.
  • Rieder, Gisèle Ruiz

Abstract

The discrete and continuous parameter forms of the mean ergodic theorem conclude that as N --> [infinity] or [tau] --> [infinity]. The ergodic limit P is shown to depend continuously on the operator T in the discrete case or on the infinitesimal generator A of the semigroup T in the continuous case. These results are motivated by recent investigations into the asymptotics of Markov chains.

Suggested Citation

  • Goldstein, Jerome A. & Rieder, Gisèle Ruiz, 1990. "Continuous dependence of ergodic limits," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 150-160, January.
    • Handle: RePEc:eee:jmvana:v:32:y:1990:i:1:p:150-160
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