L族END的多元部分和的精确大偏差下界

从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界.     

一类m-相依随机变量序列加权和的极值分布

我们将证明一类m-相依随机变量序列加权和的极值分布定理．该定理既无需i．i．d．这一假设，也不必计算协变量部分和的极限值，更没有繁杂的有关条件分布方面的假设．更重要的是该定理的结论有许多统计方面的直接应用．     

依概率收敛与依分布收敛的关系

本探讨了随机变量序列依概率收敛与依分布收敛的关系,并给出了一个依分布收敛能保证依概率收敛的最弱的条件,即：设分布函数列{Fn（x）}弱收敛于连续的分布函数F(x),则存在随机变量序列{ξn}和随机变量ξ,它们分别以{Fn（x）}和F（x）为其对应的分布函数和分面函数,且{ξn}依概率收敛于ξ。     

依概率收敛与依分布收敛的关系

本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.     

随机变量序列两种收敛性的一个注记

随机变量序列的依概率收敛必有依分布收敛,反之未必成立.若极限随机变量服从退化分布,则两种收敛等价.自然地,若这两种收敛等价,是否有极限随机变量服从退化分布?给予该问题肯定的回答.     

次线性期望下Pareto型随机变量的大数律

本文对满足Pareto分布的随机变量建立了一些大数律,从而将经典概率空间中的相关结论推广到次线性期望空间中.基于Pareto分布,获得了一些独立随机变量序列加权和的弱大数律和强大数律.     

对称随机变量部分和的概率不等式

在对称随机变量分布函数关于原点的值大于或等于二分之一的基础上,阐明对称随机变量的部分和仍是对称随机变量,进一步,给出关于对称随机变量序列部分和的概率不等式.     

整值随机变量序列的一类强律的信息条件

本文引进相对熵密度偏差作为任意整值随机变量序列相对于服从几何分布地独立随机变量序列的偏差的一种度量，并能过限制相对熵密度偏差，给出整值随机变量序列的强大数定理成立的一个充分条件。     

关于广义几何分布的强偏差定理

利用对数似然比作为一类整值随机变量序列相对于独立随机变量序列的偏差度量,在限定对数似然比的给定样本空间的子集上,建立并证明一类整值随机变量序列的强偏差定理,作为推论得到了此类分布的独立随机变量序列的若干强大数定律.     

整值随机变量序列的一类强律

本文引进似然比作为整值随机变量序列相对于服从Poisson分布的独立随机变量序列的偏差的一种度量，并通过限制似然比给出了样水空间的某种子集．在这种子集上得到了一类用不等式表示的强律，独立随机变量序列的一类强律是其特例．     

Moment Complete Convergence for Weighted Sums of -Mixing Random Variables

In this paper, the authors discuss the moment complete convergence for weighted sums of -mixing random variables, and obtains the sufficient condition for moment complete convergence of -mixing sequence under some mixing rate condition, which generalize the result of moment complete convergence for weighted sums of i.i.d. random variables to -mixing random variables.     

Improved convex upper bound via conditional comonotonicity

Comonotonicity provides a convenient convex upper bound for a sum of random variables with arbitrary dependence structure. Improved convex upper bound was introduced via conditioning by Kaas et al. [Kaas, R., Dhaene, J., Goovaerts, M., 2000. Upper and lower bounds for sums of random variables. Insurance: Math. Econ. 27, 151-168]. In this paper, we unify these results in a more general context using the concept of conditional comonotonicity. We also construct an approximating sequence of convex upper bounds with nice convergence properties.     

NA序列部分和的矩完全收敛性

讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果.     

随机变量序列加权和的强收敛性

本文讨论了一般随机变量序列加权和的强收敛性．作为推论，得到一类鞅差序列加权和的收敛定理和若干经典的独立随机变量序列的强大数定律；已有的若干结论是本文结果的特例．     

随机变量序列乘积和的矩完全收敛性

利用王岳宝等将乘积和转化为部分和的乘积之和的方法,研究了随机变量序列乘积和的矩完全收敛性,获得了乘积和矩完全收敛的充分条件.     

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This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.     

Asymptotic tail probability of randomly weighted sums of dependent random variables with dominated variation

This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result we obtain extends the corresponding result of Wang and Tang[7].     

$\rho^*$-混合随机变量列加权和的完全收敛性

In this paper, the complete convergence of weighted sums for ρ*-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ*-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. (J. Theoret. Probab., 1995, 8(1): 49-76) from i.i.d. to ρ*-mixing setting but also obtain their necessities and relax their conditions.     

Almost sure convergence of sums of maxima and minima of positive random variables

For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables.