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

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  • Frolov, Andrei N.

Abstract

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

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    1. Petrov, Valentin V., 2002. "A note on the Borel-Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 283-286, July.
    2. Endre Boros & András Prékopa, 1989. "Closed Form Two-Sided Bounds for Probabilities that At Least r and Exactly r Out of n Events Occur," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 317-342, May.
    3. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
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    Cited by:

    1. 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.
    2. Frolov, Andrei N., 2021. "On upper and lower bounds for probabilities of combinations of events," Statistics & Probability Letters, Elsevier, vol. 173(C).
    3. Stepanov, Alexei, 2014. "On the use of the Borel–Cantelli lemma in Markov chains," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 149-154.
    4. Frolov, Andrei N., 2017. "On inequalities for values of first jumps of distribution functions and Hölder’s inequality," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 150-156.

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