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Bounds for probabilities of unions of events and the Borel–Cantelli lemma


  • Frolov, Andrei N.


We discuss a method which yields new bounds for probabilities of unions of events. These bounds are stronger than the Chung–Erdős inequality and its generalizations. We derive new generalizations of the second part of the Borel–Cantelli lemma. Earlier generalizations are special cases.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2189-2197 DOI: 10.1016/j.spl.2012.08.002

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    References listed on IDEAS

    1. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
    2. Petrov, Valentin V., 2002. "A note on the Borel-Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 283-286, July.
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    Cited by:

    1. Stepanov, Alexei, 2014. "On the use of the Borel–Cantelli lemma in Markov chains," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 149-154.
    2. repec:eee:stapro:v:126:y:2017:i:c:p:150-156 is not listed on IDEAS
    3. Yang, Jun & Alajaji, Fady & Takahara, Glen, 2016. "On bounding the union probability using partial weighted information," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 38-44.


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