局部次指数随机变量和的尾分布

The Tail for Sums of Random Variables with Local Subexponential Behaviour

记S△为局部次指数分布族,F,G是S△中2个不同的局部次指数分布,Gn*表示的是G自身的n重卷积,Asmussen(2003)做了局部次指数随机变量和的尾分布的相关工作,但得到结果所需要的条件太强(E(1+ε)τ<∞亦即各阶矩都有限),考虑的是把各阶矩都有限的条件减弱,在局部长尾族上得到其随机变量和的尾分布。

Let S_△ denote the class of local subexponential distributions and F,G are different distribution in S_△,Gn＊ the n-fold convolution of distribution G.In condition of above,Asmussen（2003） did relative work about local subexponential behaviour and got its tail behaviour,but get results required conditions too strong（i.e.E（1＋ε）τ∞ all moments are limited）,considering all moments are all limited conditions is abate,get its tail distribution in L_△.