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Some dichotomy results for functionals of Harris recurrent Markov chains

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  • Chen, Xia

Abstract

Let {Xn}n[greater-or-equal, slanted]0 be a Harris recurrent Markov chain with state space E and let [xi] be a measurable map from E to a separable Banach space B and setSome integrabilities and tail behaviors of Sn over one excursion between two visits to a subset A of E are considered. It is shown that they hold either for all A in certain classes or for none in these classes.

Suggested Citation

  • Chen, Xia, 1999. "Some dichotomy results for functionals of Harris recurrent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 211-236, September.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:1:p:211-236
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    Cited by:

    1. Samur, J.D.Jorge D., 2004. "A regularity condition and a limit theorem for Harris ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 207-235, June.
    2. Xia Chen, 1999. "The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization," Journal of Theoretical Probability, Springer, vol. 12(2), pages 421-445, April.
    3. Chen, Xia, 2000. "Chung's law for additive functionals of positive recurrent Markov chains," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 253-264, April.

    More about this item

    Keywords

    Harris recurrence Small set D-set;

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