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On the use of the Borel–Cantelli lemma in Markov chains

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  • Stepanov, Alexei

Abstract

In the present paper, we propose technical generalizations of the Borel–Cantelli lemma. These generalizations can be further used to derive strong limit results for Markov chains. In our work, we obtain some strong limit results.

Suggested Citation

  • Stepanov, Alexei, 2014. "On the use of the Borel–Cantelli lemma in Markov chains," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 149-154.
  • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:149-154
    DOI: 10.1016/j.spl.2014.03.025
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    References listed on IDEAS

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    1. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    2. Petrov, Valentin V., 2002. "A note on the Borel-Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 283-286, July.
    3. Bairamov, I. & Stepanov, A., 2010. "Numbers of near-maxima for the bivariate case," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 196-205, February.
    4. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
    5. Frolov, Andrei N., 2012. "Bounds for probabilities of unions of events and the Borel–Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2189-2197.
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    Cited by:

    1. Stepanov, Alexei & Berred, Alexandre & Nevzorov, Valery B., 2016. "Concomitants of records: Limit results, generation techniques, correlation," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 184-188.

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