Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials

Takis Konstantopoulos; Zhenxia Liu; Xiangfeng Yang

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arXiv · 1507.02935

Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials

Takis Konstantopoulos·Zhenxia Liu·Xiangfeng Yang

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Abstract

The longest stretch $L(n)$ of consecutive heads in $n$ i.i.d. coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of $L(n)$ and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of $L(n)$ near its nominal value $\log_{1/p} n$ and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of $L(n)$.

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Takis Konstantopoulos, Zhenxia Liu, Xiangfeng Yang. 2015-07-10. Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials. https://arxiv.org/abs/1507.02935

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