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Large Deviation Behavior for the Longest Head Run in an IID Bernoulli Sequence

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  • Yong-Hua Mao

    (Beijing Normal University)

  • Feng Wang

    (Capital Normal University)

  • Xian-Yuan Wu

    (Capital Normal University)

Abstract

Let $$S_N$$ S N be the length of the longest 1-run in an $$N$$ N -length sequence of Bernoulli trials with parameter $$p$$ p . The famous Erdős-Rényi Law tells that $${S_N}/{\ln N}\rightarrow \xi (p)$$ S N / ln N → ξ ( p ) almost surely as $$N\rightarrow \infty $$ N → ∞ . In this paper, by deriving a sharp lower bound on $$\mathbb{P }(S_N

Suggested Citation

  • Yong-Hua Mao & Feng Wang & Xian-Yuan Wu, 2015. "Large Deviation Behavior for the Longest Head Run in an IID Bernoulli Sequence," Journal of Theoretical Probability, Springer, vol. 28(1), pages 259-268, March.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:1:d:10.1007_s10959-013-0498-8
    DOI: 10.1007/s10959-013-0498-8
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    References listed on IDEAS

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    1. James Allen Fill, 2009. "On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains," Journal of Theoretical Probability, Springer, vol. 22(3), pages 587-600, September.
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    Cited by:

    1. Tianxiang Ren & Jinwen Wu, 2023. "Percolation Problems on N -Ary Trees," Mathematics, MDPI, vol. 11(11), pages 1-14, June.

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