Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable

[摘要] 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.

[学科分类] 应用数学

[关键词] tail probability;Pareto type;Laplace-Stieltjes transform;Tauberian theorem