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Ergodicity and central limit theorems for a class of Markov processes

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  • Bhattacharya, Rabi N.
  • Lee, Oesook

Abstract

We consider a class of discrete parameter Markov processes on a complete separable metric space S arising from successive compositions of i.i.d. random maps on S into itself, the compositions becoming contractions eventually. A sufficient condition for ergodicity is found, extending a result of Dubins and Freedman [8] for compact S. By identifying a broad subset of the range of the generator, a functional central limit theorem is proved for arbitrary Lipschitzian functions on S, without requiring any mixing type condition or irreducibility.

Suggested Citation

  • Bhattacharya, Rabi N. & Lee, Oesook, 1988. "Ergodicity and central limit theorems for a class of Markov processes," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 80-90, October.
    • Handle: RePEc:eee:jmvana:v:27:y:1988:i:1:p:80-90
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    Cited by:

    1. Lee, Oesook, 1997. "Limit theorems for some doubly stochastic processes," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 215-221, March.
    2. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.

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