关于分布极限类的一些讨论

早在本世界上半叶,人们就已彻底弄清楚了 uan 条件之下(即一致渐近可忽略条件)的独立和的分布极限类,建立起了较为完整的无穷可分分布理论。根据这个理论,只有无穷可分分布才有可能成为 uan 条件之下的独立和的极限分布,并且只有稳定律才有可能成为独立同分布随机变数列{x_n}的正则化部分和{1/(B_n)S_n-A_n}的极限分布。但     

一类特殊Weibull分布纪录值之和的中心极限定理

给出了参数τ为正整数的倒数为Weibull分布纪录值之和的中心极限定理。     

U-统计量渐近正态余项级数的收敛性

的收敛性,并获得了园满的结果,在独立和情况下的同一问题,曾由 Heyde[2]于1966年讨论。本文将反复引用[2]中的结果,本文的主要结果是:     

关于多维无穷可分分布的Lebesgue分解

In this paper we have investigated and proved various Lebesgue properties of the n-dimensional quasi-distributions. 2-dimensional quasi-distributions have been classified into 5 types. It is proved among others that every 2-dimensional quasi-distribution can be expressed uniquely as a sum of 5 functions belonging to different types. Some necessary and sufficient conditions for functions belonging to each given type have been analysed in detail.     

A note on asymptotic behavior for negative drift random walk with dependent heavy-tailed steps and its application to risk theory

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ ∞∑j=-∞ψn-jεj, where {ε, εn; -∞＜ n ＜ ∞}is a sequence of independent, identically distributed random variables with zero mean, μ＞0 is a constant and the coefficients {ψi;-∞＜ i ＜∞} satisfy 0 ＜∞∑j=-∞|jψj| ＜∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ ∞∑j=-∞εjβnj) ＞ x}is discussed. Then the result is applied to ultimate ruin probability.     

关于DRCE随机阵列的若干极限性质

本文充分利用了ＤＲＣＥ随机变量阵列的特殊结构，在强大数律和ｒ－＝阶矩收敛速度方面，取得了类似ｉｉｄ，序列的结果；并在适当的条件下证明了完全收敛性。     

On the Pointwisise L_p Convergence Rates of Nearest Neighbor Estimate of Nonparametric Regression Function

Let (X,y) be a R~d×R~1-valued radom vector with E(?)=E(Y|X=x) be the regression funvion of Y with respect to X.Su (X_i, Y_i),i=1, …,n, are iid samples drawn ftc, from (X,Y).(?)desired to estimate m(x) based on these samples,everoye discussed in (?) the pointwise convergence of the nearest neigthoor estimate m_n(X) (see (5) of the present paper). Ih this article we further study the rate of this eonyer-gence.It is shown that if there exists p≥2 sach that E 、|Y|<∞,then for suitabte choice of the weighte C_m (see(4) of the present paper).     

关于U统计量的一点注记

Let φ(x₁,x₂,…x_m) be a real Borel measurable symmetrical function of the m variables, and let U_n denote the U-statistic with kernel φ. In this note it is proved that the necessary and sufficient condition for E|φ|<+∞ is that there exists an n≥m such that E|U_n|< + ∞.     

独立随机变量乘积的分布性状

设X与Y为相互独立的非负随机变量, 考察乘积XY的尾分布性状. 可将X视为初始资本, 而Y则是利率的影响. 在现代金融保险业中, 通常假定X属于一定的分布族, 而要考虑的问题是: Y的尾分布性状会对XY的尾性状产生怎样的影响? 在怎样的条件下, XY能够保持X的原有族性? 探讨了当X的分布属于L族和S族时, XY的分布仍能属于相应分布族的条件, 这些条件远远弱于既往文献中所给出的条件. 同时还证明了: 当X服从L(γ) (γ>0)族连续分布时, XY的分布属于L族的充要条件是Y为无界随机变量.     

U-统计量的精致渐近性

设{X_n．n≥1}是一非退化的i．i．d．随机变量序列,U_n是以二维Borel可测对称函数h(x,y)为核函数的U-统计量．记U_n=2/(n(n-1))Σ_≤i≤j≤nh(X_i,X_j)．本文分别在核函数h(x,y)只有4/3阶矩或4/3+δ,0＜δ≤1的情况下,对非常广泛的一类权函数(x)与边界函数b(x)得到了如下关于U-统计量U_n的精致渐近性:不仅使得已有的结果成为我们的特况,还大大降低了其中的矩条件．