两两独立同分布序列Cesàro强大数定律的收敛速度

设{X,Xn,n≥0}是两两独立同分布的随机变量序列,11．为了证明这一结论而获得到的两两负相关随机变量序列的Cesaro强大数定律收敛速度的结果本身也是有意义的．此结果对于同分布的两两NQD序列也是对的．     

两两NQD列的强大数定律

该文把同分布的两两NQD列的Kolmogorov强大数定律推广到了在一类广泛的条件下的不同分布的情形, 为此而建立的Kolmogorov Chung型强大数定律本身也是有意义的.      

两两独立序列加权和的L~r收敛性

讨论了两两独立随机变量列加权和在满足r(1≤r<2)阶Ces`aro一致可积条件下的Lr收敛性,获得了与独立情形一致的结果.用相似的方法,对于其它相依或混合序列(如两两NQD列,φ-混合序列,ρ-混合序列)也有相同的结果.     

THE ERDOS-RENYI LAWS OF LARGE NUMBERS FOR NON-IDENTICALLY DISTRIBUTED RANDOM VARIABLES

The Erdos-Renyi law of large numbers (1970) is the first important result forasymptotic behaviours of increments of partial sams of a sequence of random variableswith apan [ClogN]. Some generalizations have been done sinoe then, such as conver-gence rate of the limit, some results when order of span being either higher or lowerthan log N. But all these results are only obtained in the case of i. i. d. random variables.This paper aims at the generalization of these results to the ease when random variablesare independent, but not necessarily identically distributed. To this end Chernoff Theoremis generalized to the corlesponding case at first.     

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.     

分块m-负相依随机变量的Wittmann 型强大数律

本文得到了分块m-负相依随机变量的Wittmann 型强大数律,这些结果推广和改进了已知的一些文献中相关的结论.     

不同分布两两NQD列的一类强大数定律

本文对一类相当广泛条件下的不同分布两两NQD列的部分和及乘积和强大数定律进行讨论,在更弱的条件下,推广了已有的几个最新结果,使之成为本文结论的推论,所得结论更具优越性,这些结论都是独立情形经典结果的推广.     

同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

关于两两NQD随机变量部分和强大数律的注记

In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et al. （2013）, and Qiu and Yang （2006） under some weaker conditions.     

Strong Laws for Martingale Differences and Independent Random Variables

A strong law of large numbers (SLLN) for martingale differences {X _n,_n,n1} permitting constant, random or hybrid normalizations, is obtained via a related SLLN for their conditional variances E{X _n ² |_n-1}n1. This, in turn, leads to martingale generalizations of known results for sums of independent random variables. Moreover, in the independent case, simple conditions are given for a generalized SLLN which contains the classical result of Kolmogorov when the variables are i.i.d.     

随机变量的截尾与几个经典强大数定律的推广

利用随机变量的截尾方法和条件三级数定理这一工具研究任意随机变量序列的性质,得到了矩条件下任意随机变量序列的一类强极限定理和强大数定律以及一些简单实用的结论,推广了与此相应的一些结果和若干经典的强大数定律.     

Strong Laws of Large Numbers for Random Walks in Random Sceneries

In this paper, we study strong laws of large numbers for random walks in random sceneries. Some mild sufficient conditions for the validity of strong laws of large numbers are obtained.     

B值随机变量序列的强极限定理和强大数定律

利用鞅收敛定理,讨论了B值随机变量序列的强收敛性,得到了一类强极限定理和强大数定律,使某些已知结果为其特例。     

两两NQD随机序列的 Lr 收敛性

该文讨论了两两NQD随机变量列在满足$r(1\leq r<2)$阶Ces\`aro一致可积条件下的 L^r 收敛性,获得了与独立情形一致的结果.     

Large Deviations for Sums of Independent Heavy-Tailed Random Variables

We obtain precise large deviations for heavy-tailed random sums , of independent random variables. are nonnegative integer-valued random variables independent of r.v. (X _i )i N with distribution functions F _i. We assume that the average of right tails of distribution functions F _i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given.     

混合序列的强大数律

讨论了混合序列部分和的强收敛性,所得结果推广和改进了文献[1]、[2],并推广了Marcinkiewicz强大数律．     

On the Law of Large Numbers for Weakly Dependent Random Variables

In this paper, we present the Hsu–Robbins and Spitzer law of large numbers for m-dependent and -mixing random variables. In the main theorems, we do not assume that the random variables are identically distributed.     

两两NQD随机序列的L^r收敛性

该文讨论了两两NQD随机变量列在满足r(1≤ r＜2)阶Cesàro一致可积条件下的Lr,收敛性,获得了与独立情形一致的结果.