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

Applications of mathematics

Nakagawa, Kenji¹ 

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

DOI  :  10.1007/s10492-015-0089-3

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 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.

【 授权许可】

Unknown