ρ-混合序列部分和的精确渐近性

设{X_n;n≥1}是均值为零的严平稳ρ-混合序列,利用ρ-混合序列的弱收敛定理及概率不等式,在适当的矩条件下,得到了ρ-混合序列部分和的精确渐近性的一般结果.     

混合序列加权和的强大数定律

设{Xn,n≥1}是同分布随机变量序列,{αnk,n≥1,1≤k≤n}是满足某种条件的常数序列.本文在ψ-混合,ρ-混合,ρ~-混合条件下讨论了加权和∑kn=1ankXk的Kolmogorov强大数定律.     

ρ-混合序列完全矩收敛精确渐近性的一般结果

设{X,X_n;n≥1}是均值为零的严平稳ρ-混合随机变量序列.在适当的条件下,利用ρ-混合序列的弱收敛性和矩不等式,证明了其完全矩收敛精确渐近性的一般结果,改进并推广了已有的结果.     

相依随机变量的密度函数的递归核估计的渐近正态性

设{X_n;n≥1}为同分布的ρ-混合序列,其未知密度,f(x)的递归核估计为: f_n(x)=1/n sum from j=1 to n h_j~(-1)K(x-X_j/h_j),本文在适当的条件下,讨论由f_n(x)所产生的随机元的有限维渐近正态性。     

ρ-混合序列的重对数律

设{Xn,n≥1}是同分布ρ-混合序列,其分布属于特征指数为α(0<α<2) 的非退化稳定分布的正则吸引场,证明了依概率1有lira supn→∞ = e1/α,并获得了一系列等价条件．此结果的获得不仅将已有的一些结果推广至ρ-混合序列的情形,并且将其结果作了一定的改进．     

关于具有三个不同素因子的盈不完全数（英）

设ρ是可乘算术函数,定义为对每个素数方幂p~α,ρ(p~α)=p~α-p~(α-1)+p~(α-2)-…+(-1)~α.对正整数n,若2ρ(n)=n+d,其中d是n的真因子,则称n为盈因子是d的盈不完全数.本文得到了具有三个不同素因子的所有奇盈不完全数和部分偶盈不完全数.     

关于线性算子的高阶饱和

设f(x)∈C_(2π)。而f(x)～sum from k=0 ( )A_k(f_1k)≡α_0/2 sum from k=1 ( )(α_kcoskx b_ksinkx)。 又设 U_n(f,x)=1/πintegral from -πto π(f(x t)u_n(t)dt,) 其中u_n(t)=1/2 sum from k=1ρ_k~(n)coskt满足条件: integral from 0 to k(|u_n(t)|dt=O(1),)ρ_k~(n)→1(n→∞;k=1,2,…,)。设m是正整数,ρ_0~(n)=1。记~mρ_k~(n)=sum form v=0 to ∞ ((-1)~(m~(-v))(m v)ρ_k v~(n) (k=0,1,…,)。)T.Nishishiraho考虑了在ρ_k~(n)=O(k>n)的情况下U_n(f,x)的饱和问题,证明了。 定理A 设{_n}是收敛于0的正数列,使得     

E^n中Euler不等式的推广

设 n 维欧氏空间 E~n 中 n 维单形 Ω 的外接球半径为 R,内切球半径为 r,M.S.Klamkin 获得 E~n 中之 Euler 不等式:R≥nr.本文给出 E~n 中 Euler 不等式的下述几个推广:(i)R~2≥δ_nn~2r~2+(?);(ii)R~2≥(?)/2(1+δ_n)n~2r~2+(1/2)(?);(iii)R~2≥n~2r~2+(1/4)(?)其中 I、O、G 分别为单形Ω的内心、外心与重心,δ_n=(?)[1-((ρ_(ij)-ρ_(jk))~2(ρ_(jk-ki))~2(ρ_(ki)-ρ_(ij))~2)/(ρ_(ij)ρ_(jk)ρ(k(?)))]~((-1)/n(n~2-1))≥1,ρ_(ij)=(?)(1≤i相似文献   

任意体上矩阵的ρMoore-Penrose逆的某些显式

设K是一个任意的体,表示K上所有矩阵的集合,K~(m×n)表示K上m×n矩阵的集合,K_r~(m×n)={A∈K~(m×n)|RankA=r}.推广[1]中的概念,我们引入定义1.设的一个变换,如果满足 (i)(AB)~ρ=B~ρA~ρ,A∈K~(m×n),B∈K~(?); (ii)(A~ρ)~ρ=A,A∈, 那么ρ叫做的一个对合函数. 定义2.设ρ是的一个对合函数,A∈K~(m×n),如果存在X∈K~(n×m),满足下面关于ρ的Penrose方程:     

混合序列部分和的强大数定律

设{Xn，n≥1）是ρ^-混合序列．利用随机变量的截尾方法和ρ^-混合序列的三级数定理这一工具研究了ρ^-混合序列的性质。得到了矩条件下ρ^-混合序列的—类强极限定理和强大数定律。并给出了一些简单应用。推广了若干经典的强大数定律．     

混合序列强大数定律的收敛速度

混合序列强大数定律的收敛速度薛留根（河南许昌师范高等专科学校数学系，许昌４６１０００）河南省自然科学基金资助项目．１９９０年１２月３日收到，１９９１年１１月１１日收到第一次修改稿．一、引言和引理关于独立同分布的随机变量序列｛Ｘｎ｝的强大数定律的收敛速...     

不同分布ρ混合序列乘积和的强收敛性

研究了ρ混合序列的收敛性质,利用得到的结果和ρ混合序列的矩不等式讨论了ρ混合序列乘积和的强收敛性质.     

不同分布φ混合序列乘积和的强收敛性

利用φ混合序列矩不等式讨论了φ混合亭列乘积和的强收敛性质．     

Upper Large Deviations for Mixing Random Sequence

In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.     

Sequences of elliptical distributions and mixtures of normal distributions

Two conditions are shown under which elliptical distributions are scale mixtures of normal distributions with respect to probability distributions. The issue of finding the mixing distribution function is also considered. As a unified theoretical framework, it is also shown that any scale mixture of normal distributions is always a term of a sequence of elliptical distributions, increasing in dimension, and that all the terms of this sequence are also scale mixtures of normal distributions sharing the same mixing distribution function. Some examples are shown as applications of these concepts, showing the way of finding the mixing distribution function.     

Banach空间上的强混合算子

1999年,L．B．Gonzalez 证明了任意无限维可分 Banach 空间上存在拓扑传递的有界线性算子．这个结果肯定地回答了 S．Rolewicz 提出的问题．本文证明了由 L．B．Gonzalez 所给出的算子实际上是强混合的,同时,对加权移位算子的混合性利用权序列进行了刻划并指出任意无限维可分 Hilbert 空间上存在弱混合而非强混合的有界线性算子．     

Tightness bounds for strongly mixing random sequences

For a given strictly stationary, strongly mixing random sequence for which the distributions of the partial sums are tight, certain ``tightness bounds" exist which depend only on the marginal distribution and the mixing rate.

     

Strong law for mixing sequence

In this article we present some theorems on the strong law for the mixing sequence which is not necessarily stationary, with the mixing coefficient involving only a pair of variables in the sequence.Research sponsored by the Air Force Office of Scientific Research under Contract F 49620-85-C-0008. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.This author is also supported by National Natural Science Foundation of China.     

Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences.     

Some mixing properties of tukey's 3R smoother †

Suppose Tukey's 3R (“running median”) smoothing algorithm is applied to a strictly stationary sequence X: = (X_k) of random variables, thereby creating a new stationary sequence X? If X satisfies the strong (Rosenblatt) mixing condition, then so does .X? If X is an i.i.d. sequence with each X(_k:) uniformly distributed on the interval [0,1], then X? fails to be (mixing. Thus two questions of C. Mallows are answered.