正则和函数的强极限及应用

研究了随机变量序列正则和函数的重对数律,作为应用,给出了正的随机变量序列部分和乘积的重对数律.同时,还获得了独立随机变量阵列相应的单对数律结果.     

关于NA随机变量极限定理的注记

NA随机变量是一包含独立随机变量在内的有广泛应用的随机变量类,本文在一些更弱的条件下,建立了具有不同分布NA随机变量列的强大数律和有界重对数律,进而推广了已有的关于NA随机变量的结果。     

关于ρ-混合序列对数律的收敛速度

本文研究了ρ-混合序列对数律的收敛速度，在较弱的矩条件下得到了与独立同分布实随机变量类似的结果，并获得了ρ－混合序列满意对数律的一个充分性结果；讨论了ρ－混合序列重对数律的收敛速度的问题，得到了一个重对数律的充分性条件。     

非同分布NA列的对数律和重对数律

给出了非同分布NA列满足对数律和重对数律的一些矩条件，而文[50-[7]中的部分结果可以成为其特殊情形并得到加强．     

关于可交换随机变量序列的重对数律

本文讨论了可交换随机变量序列{Xn:n≥1}的重对数律。     

可交换随机变量序列重对数律的收敛速度

本文讨论了可交换随机变量序列{Xn:n≥1)重对数律的收敛速度,得到了可交换随机变量序列与独立序列类似的极限性质,同时给出了可交换序列重对数律收敛速度的一种描述.     

Banach空间中独立不同分布随机变量的重对数律及其应用

对B-值独立不同分布随机变量, 证明了一个一般的重对数律. 作为应用, 建立了Hilbert型自回归过程经验算子的重对数律.     

Fuk-Nagaev型不等式的推广及应用

本文首先对具有ｐ（１〈ｐ≤２）阶矩的独立Ｂ值随机变量列（Ｘｎ）研究了Ｆｕｋ－Ｎａｇａｅｖ型不等式,进而得出重对数律的一些结果。     

关于非强平稳NA列的重对数律及其应用

本文讨论了非强平稳ＮＡ（ＮｅｙａｔｉｖｅｌｙＡｓｓｏｃｉａｔｅｄ）列的若干重对数律,并用以估计线性模型中ＮＡ误差的方差估计的一类强收敛速度．     

NA随机变量列的有界重对数律

通过建立NA随机变量最大部分和的一些概率指数不等式，给出了具有不同分布的NA随机变量列有界重对数律的一些结果，因此推广了由R．Wittmann建立的独立随机变量的相关结果。     

The law of the iterated logarithm for positively dependent random variables

The Levy's type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables. Unfortunately, this type inequality cannot be obtained for a generalization of association, i.e., linear positive quadrant dependence, because of their special dependence structure. The purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables.     

A LIL for independent non-identically distributed random variables in Banach space and its applications

In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.     

线性模型的最小二乘估计的中偏差及其重对数律

本文研究了线性模型的最小二乘估计的中偏差.通过估计Laplace渐近积分,得到了随机误差为取值于Rd的相互独立同分布随机变量情形下的中偏差与重对数律的结果.     

The Law of the Iterated Logarithm for Weakly Dependent Hilbert Space Valued Random Variables

We consider the bounded and compact laws of the iterated logarithm for weakly dependent Hilbert space valued random variables. Under optimal moment conditions, we prove the bounded and compact laws of the iterated logarithm for sequences of identically distributed Hilbert space valued random variables satisfying the uniform strong mixing condition.     

NA序列重对数律的几个极限定理

设{X_n;n≥1}均值为零、方差有限的NA平稳序列。记S_n=∑_(k=1)~n X_k,M_n=maxk≤n|S_k|,n≥1.假设σ~2=EX_1~2+2∑_(k=2)~∞EX_1X_k>0。本文讨论了:当ε 0时,P{M_n≥εσ(2nloglogn)~(1/2)的一类加权级数的精确渐近性质,以及当ε∞时,P{M_n≤εσ(π~2n/(8loglogn))~(1/2)}的一类加权级数的精确渐近性质。这些性质与重对数律和Chung重对数律的速度有关。     

LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT＊

In this article,we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d.random environments.     

On the law of the iterated logarithm for Gaussian processes

We present some optimal conditions for the compact law of the iterated logarithm of a sequence of jointly Gaussian processes in different situations. We also discuss the local law of the iterated logarithm for Gaussian processes indexed by arbitrary index sets, in particular for self-similar Gaussian processes. We apply these results to obtain the law of the iterated logarithm for compositions of Gaussian processes. Research partially supported by NSF Grant DMS-93-02583.     

负相伴随机变量的非经典重对数律

§ 1　 IntroductionA finite family of random variables { Xi,1≤ i≤ n} is said to be negatively associated(NA) is for every pair of disjointsubsets A1 and A2 of{ 1 ,2 ,...,n} ,Cov{ f1 (Xi,i∈ A1 ) ,f2 (Xj,j∈ A2 ) }≤ 0 ,(1 .1 )whenever f1 and f2 are coordinatewise increasing and the covariance exists.An infinitefamily is negatively associated ifevery finite subfamily is negatively associated.This defini-tion was introduced by Alam and Saxena[1 ] and Joag-Dev and Proschan[2 ] .As pointed…     

A functional law of the iterated logarithm for associated sequences

Recently, a functional central limit theorem and a Berry-Essen Theorem have been demonstrated for classes or associated random variables. Using these results, and similar results for multiplicative sequences, we show a functional law of the iterated logarithm for associated sequences satisfying a rate requirement.