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Invariant probability measures for a class of Feller Markov chains

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  • Costa, O. L. V.
  • Dufour, F.

Abstract

In this paper we consider a Markov chain defined on a locally compact separable metric space which satisfies the Feller property. We introduce a new assumption which generalizes T-chain and irreducibility assumptions, well known in the literature of Markov chains. Under this new assumption, the Foster's criterion is shown to be equivalent to the existence of an invariant probability measure for Feller-Markov chains, which is also equivalent to the existence of a non-singular invariant probability measure.

Suggested Citation

  • Costa, O. L. V. & Dufour, F., 2000. "Invariant probability measures for a class of Feller Markov chains," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 13-21, October.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:1:p:13-21
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    References listed on IDEAS

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    1. Lasserre, Jean B., 1997. "Invariant probabilities for Markov chains on a metric space," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 259-265, June.
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    Cited by:

    1. Costa, O. L. V. & Dufour, F., 2001. "Necessary and sufficient conditions for non-singular invariant probability measures for Feller Markov chains," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 47-57, May.
    2. Costa, O.L.V. & Dufour, F., 2005. "On the ergodic decomposition for a class of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 401-415, March.
    3. Tweedie, R. L., 2001. "Drift conditions and invariant measures for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 345-354, April.

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