广义次指数族的卷积根的封闭性

The Closure of an Extensive Subexponential Distribution Class under Convolution Roots

设F是支撑在(-∞,∞)上的分布函数.v是一个取有限个整数值的非负随机变量,F*v为F的v重卷积.在一定条件下,本文得到了如下结论:对任意0≤γ<∞,F*v∈S(γ)F∈S(γ).特别地,若v≡n,n≥2,本文得到了支撑在(-∞,∞)上的S(γ)族的卷积根的封闭性.上述所得结果推广了[2]对应结果.

Let F on （- ∞,∞） be a distribution function and F#v is the v- fold convolution of F, where v is a nonnegative random variable taking only a finite number of integer-values. Under certain conditions,the paper obtains the following result.for any 0≤ y∞,F#v S（y）→←F∈S（7）. Particularly ,if v≡n ,n≥ 2, we give the closure of S（7） under convolution roots supported on （- ∞,∞）. The above obtained results extend the corresponding results of E23.