Geodesic
Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable
Applications of Mathematics, Tome 60 (2015) no. 2, pp. 157-184.

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We give a sufficient condition for a non-negative random variable $X$ to be of Pareto type by investigating the Laplace-Stieltjes transform of the cumulative distribution function. We focus on the relation between the singularity at the real point of the axis of convergence and the asymptotic decay of the tail probability. For the proof of our theorems, we apply Graham-Vaaler's complex Tauberian theorem. As an application of our theorems, we consider the asymptotic decay of the stationary distribution of an M/G/1 type Markov chain.
DOI : 10.1007/s10492-015-0089-3
Classification : 30D10, 40E05, 42A38, 60F99
Keywords: tail probability; Pareto type; Laplace-Stieltjes transform; Tauberian theorem 
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     title = {Tail probability and singularity of {Laplace-Stieltjes} transform of a {Pareto} type random variable},
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Nakagawa, Kenji. Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable. Applications of Mathematics, Tome 60 (2015) no. 2, pp. 157-184. doi : 10.1007/s10492-015-0089-3. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0089-3/

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