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

Yong-Hua Mao (), Feng Wang () and Xian-Yuan Wu ()
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Yong-Hua Mao: Beijing Normal University
Feng Wang: Capital Normal University
Xian-Yuan Wu: Capital Normal University

Journal of Theoretical Probability, 2015, vol. 28, issue 1, 259-268

Abstract: 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

Keywords: Head-run; Large deviation; Hitting time; Skip-free Markov chain; 60F10; 60J10 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0498-8

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