卷积等价分布族的封闭性

Closure of families of convolutional equivalent distributions

研究卷积等价分布族关于卷积运算的封闭性是应用概率论中的一个基本理论问题。本文类比次指数分布族在其运算下的封闭性,首先给出卷积等价分布族关于卷积封闭的若干充要条件。在此基础上,设X,Y是两个相互独立的实值随机变量,最后分别给出了max(X,Y)关于卷积等价分布族封闭的充要条件以及min(X,Y)关于卷积等价分布族封闭的充分条件。

It is a basic theoretical problem in applied probability theory to study the closure of convolution operation of the class of convolution equivalent distributions.The paper compares the closure of subexponential distributions under convolution operation and some necessary and sufficient conditions for closure property under convolution operation about the class of con-volution equivalent distributions are firstly presented.Based on these results,assuming that X and Y are two independent real-val-ued random variables,a necessary and sufficient condition for closure property of max(X,Y)and then a sufficient condition for closure of min(X,Y)about the class of convolution equivalent distributions are given respectively.