On the Singularity of Laplace-Stieltjes Transform of a Heavy Tailed Random Variable

摘要

In this paper, we give a sufficient condition for a non-negative random variable X being heavy tailed. A light tailed case is studied in [5]. The sufficient condition is an analytic property of Laplace-Stieltjes transform of the probability distribution function of X. The proof is based on the complex Tauberian theorem by Graham-Vaaler [1].