Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

Kenji Nakagawa

doi:10.1109/tit.2007.903114

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Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

Kenji Nakagawa

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Abstract

We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a theorem, according to which if the abscissa of convergence of the LS transform is negative finite and the real point on the axis of convergence is a pole of the LS transform, then the tail probability decays exponentially. For the proof of the theorem, we extend and apply so-called a finite form of Ikehara's complex Tauberian theorem by Graham-Vaaler.

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Kenji Nakagawa. 2006-02-25. Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable. https://doi.org/10.1109/tit.2007.903114

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