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Invariant probabilities for Markov chains on a metric space

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  • Lasserre, Jean B.

Abstract

We consider Markov kernels on a locally compact separable metric space that satisfy the (weak) Feller property. We provide a very simple necessary and sufficient condition for existence of an invariant probability measure. We also prove that every Feller Markov kernel on a compact Hausdorff (not necessarily metric) has an invariant probability measure. An alternative sample-path criterion of existence is also provided, as well as a sufficient condition for uniqueness.

Suggested Citation

  • Lasserre, Jean B., 1997. "Invariant probabilities for Markov chains on a metric space," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 259-265, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:3:p:259-265
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    Cited by:

    1. 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.
    2. 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.
    3. Jaroszewska, Joanna, 2013. "On asymptotic equicontinuity of Markov transition functions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 943-951.

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