强大数定律成立的充要条件

定理 设是任意随机变量序列,则强大数定律对之成立,即的充公必要件是 证明 充公性 令因为,所以由Borel-Cantelli引理即得     

随机弱大数定律和随机强大数定律的充要条件

本文讨论随机大数定律，得到随机变量序列分别服从随机弱大数定律和随机强大数定律的充要条件。     

次线性期望下弱负相关随机变量的性质及其强大数定律

强大数定律是非可加概率(或非线性期望)框架下的重要理论.目前己有许多有关非可加概率(或非线性期望)下独立同分布或负相关随机变量序列的强大数定律的研究文献.本文在非可加概率和次线性期望框架下,引入弱负相关随机变量的概念,并研究了弱负相关随机变量的有关性质.作为应用,本文还证明了弱负相关随机变量序列的强大数定律.     

B值随机变量序列的局部收敛性及大数定律

本文主要讨论了Ｂ值随机变量序列的局部收敛及大数定律与Ｂａｎａｃｈ空间几何特征的依赖关系，同时用Ｂ值随机变量序列的局部收敛性及大数定律刻划了Ｂａｎａｃｈ空间的一致光滑性。     

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．     

次线性期望下大数定律的收敛速率（英文）

在本文中,我们研究次线性期望下独立同分布随机变量的大数定律的收敛速率.我们给出了大数定律的一个强L~p收敛版本和一个强拟必然收敛版本.     

次线性期望空间下独立同分布序列的一个强大数定律

利用与概率空间不同的研究方法,研究次线性期望空间中独立同分布随机变量序列的加权和在某些条件下的一个强大数定律,从而将该定理从传统概率空间扩展到次线性期望空间.     

φ混合序列的强大数律

讨论了不同分布φ混合序列的强大数律,推广了Kolmogorov强大数定律和Marcinkiewicz强大数定律.     

■混合序列的强大数律

讨论了不同分布■混合序列的强大数律,推广了Kolmogorov强大数定律和Marcinkiewicz强大数定律.     

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.     

正相协列乘积和的重对数律与强大数律

证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律,指出了部分和服从强大数律但乘积和未必服从强大数律这一事实,并讨论了定理2中一个条件的必要性．     

随机变量序列的大数定律及常返性定理

对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律.     

关于渐近循环马氏链泛函的强大数定律

研究了一类非齐次马氏链———渐近循环马氏链泛函的强大数定律,首先引出了渐近循环马氏链的概念,然后给出了若干引理.利用了渐近循环马氏链关于状态序偶出现频率的强大数定理给出并证明了关于渐近循环马氏链泛函的强大数定律,所得定理作为推论可得到已有的结果.     

完全区间树顶点数目的大数律

本文讨论完全区间树顶点数目Sx的大数律,所采用的方法不同于单边区间树．文章包括三部分内容:首先探讨完全区间树所得以定义的概率空间,弄清楚它的结构,为强大数律的研究奠定理论基础．接着,针对完全区间树上的Sx的矩母函数不易求得的情况,另辟蹊径,求得Sx的期望和方差．最后,给出Sx的强弱大数律．     

The laws of large numbers for Pareto-type random variables under sub-linear expectation

In this paper, some laws of large numbers are established for random variables that satisfy the Pareto distribution, so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space. Based on the Pareto distribution, we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.     

A generalized strong law of large numbers

Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This law is an example of a strong law of large numbers for Borel measurable nonseparably valued elements of a metric space. Received: 24 February 1998 / Revised version: 3 January 1999     

An Extension of the Kolmogorov–Feller Weak Law of Large Numbers with an Application to the St. Petersburg Game

The Kolmogorov–Feller weak law of large numbers for i.i.d. random variables without finite mean is extended to a larger class of distributions, requiring regularly varying normalizing sequences. As an application we show that the weak law of large numbers for the St. Petersburg game is an immediate consequence of our result.     

Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition

This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables, the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.     

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??Examining the conditions of positively or negatively associated sequences of random variables obeying the strong law of large numbers provided by Alexander, the sequences of Gaussian random variables, nonnegative and uniformly bounded sequences of random variables with general dependent structure were studied, and the sufficient conditions for they obeying the strong law of large numbers were given. At last, an example for Gaussian sequence satisfying the strong law of large numbers was given.     

Law of large numbers for non-additive measures

Our aim is to establish law of large numbers for classes of non-additive measures. For balanced games we obtain weak and strong law of large numbers for bounded random variables. A sharper result is obtained for exact games. We also provide an extension to upper envelope measures.