正递减分布及其相关分布类在相依性下的闭包性质
Closure properties in positively decreasing and related distributions under dependence
AI总结：
本文研究正递减分布类在不同相依结构下的闭包性质，涵盖最小、最大、卷积等运算，并引入广义长尾正递减分布类，探讨随机停止和的封闭性及随机向量的闭包性质。
摘要：
我们考虑正递减分布类中的闭包性质。我们的结果源于不同类型的相依性，但每种类型都属于渐近独立的相依结构族。具体而言，我们考察了关于最小值、最大值、卷积积和卷积的闭包性质。此外，我们考虑了广义次指数正递减分布类的一些闭包性质，同时引入并研究了广义长尾正递减分布类。我们还重新审视了次指数性在次指数正递减类情形下的（独立）卷积闭包问题。在某些类中，我们讨论了随机停止和的封闭性。在最后一节，我们研究了两类随机向量关于最小值的闭包性质。
英文摘要：
We consider closure properties in the class of positively decreasing distributions. Our results stem from different types of dependence, but each type belongs in the family of asymptotically independent dependence structure. Namely we examine the closure property with respect to minimum, maximum, convolution product and convolution. Furthermore, we take into account some closure properties of the class of generalized subexponential positively decreasing distributions, as also we introduce and study the class of the generalized long-tailed positively decreasing distributions. Also we revisited the (independent) convolution closure problem of subexponentiality, in the case of subexponential positively decreasing class. In some classes we discuss the closedness of randomly stopped sums. In the last section we study the closure property with respect to minimum for two classes of random vectors.
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