随机变量序列加权和的强收敛性

本文讨论了一般随机变量序列加权和的强收敛性．作为推论，得到一类鞅差序列加权和的收敛定理和若干经典的独立随机变量序列的强大数定律；已有的若干结论是本文结果的特例．     

两两NQD列的一个强大数定律

本文研究了一类广泛的随机变量序列两两NQD列的收敛性质，推广了与独立情形相类似的一些强大数定律，得到了新的结果．     

非参数回归模型最小一乘估计的全局最优收敛速度

非参数回归模型最小一乘估计的全局最优收敛速度施沛德（中国科学院系统科学研究所，北京１０００８０）国家自然科学基金资助课题．１９９１年１１月２７日收到．一、引言考虑非参数回归模型这里为．随机误差序列，其分布的中位数为零；Ｘ１，Ｘ２，…为服从分布密度ｆ的...     

随机狄里克莱级数的收敛性

该文是利用随机变量序列的局部收敛性及强大数定律研究了随机狄里克莱级数的收敛性,得出了它的收敛横坐标的简洁公式．     

φ-混合随机变量序列收敛性质的若干新结果

本文将Kolmogorov型不等式推广到φ-混合序列,并且研究其强收敛性质,得到了φ-混合序列的Khintchine-Kolmogorov型收敛定理、三级数定理和Marcitlkiewicz型强大数定律.     

关于任意随机变量序列的一类强极限定理

本文的目的是建立一类任意随机变量序列的强极限定理，作为推论，得到了一类鞅差序列收敛定理，马氏过程的强极限定理和若干经典的独立随机变量序列的强大数定律，已有的若干轶差序列收敛定理和可列非齐次马氏链的一个强极限定理是本文结果的特例，本文的主要结果对随机变量序列除矩条件外没有任何要求．     

B-值随机场强大数定律的收敛速度

本文研究B-值随机场强大数定律成立的条件、强大数定律的收敛速度以及部分和序列最大值的矩问题。同时,本文还得到了完全收敛的一个充分条件。     

Chung型强大数定律及其应用

利用逐项积分对Chung型强大数定律进行简单化证明,证明既不需要鞅收敛定理,也不需要三级数定理.应用Chung型强律,得到了随机序列的若于强大数定律和收敛速度等,这些定理和推论推广了Cantrell-Rosalsky强大数定律以及由Freedman(1974)建立的关于收敛速度的结果.这些结果除矩条件外,对随机变量的独立性和联合分布不作任何要求.     

可列非齐次马氏链泛函的一类强大数定律

本文用分析方法研究可列非齐次马氏链的泛函的极限性质，得到了一类不同形式的强大数定律，在其中通常形式的强大数定律中的数学期望被条件期望所代替，关于独立随机变量序列的若干经典强大数定律是本文结果的推论．     

两两PQD序列的一个收敛性质

研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

Φ混合AR(1)过程a.s.收敛性

本文对混合变量生成的一阶自回归过程建立了Ｍａｒｃｉｎｋｉｅｗｉｃｚ强大数定律．我们还给出了Ｈａｒｔｍａｎ－Ｗｉｎｔｎｅｒ重对数律在ＡＲ（１）上的结果．     

On complete convergence for strong mixing sequences

In this paper, some results on complete convergence for strong mixing sequences are presented under some suitable conditions. A Marcinkiewicz–Zygmund-type strong law of large numbers is also obtained.     

Conditional independence,conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned.     

ψ－混合序列大数律的收敛速度

在不加任何矩条件限制的情形下，研究了ψ－混合序列大数律的收敛速度问题，得到了若干充分必要条件．     

Convergence Rates in the Law of Large Numbers under Sublinear Expectations

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong L^p-convergence version and a strongly quasi sure convergence version of the law of large numbers.     

Law of large numbers and central limit theorem for randomly forced PDE's

We consider a class of dissipative PDE's perturbed by an external random force. Under the condition that the distribution of perturbation is sufficiently non-degenerate, a strong law of large numbers (SLLN) and a central limit theorem (CLT) for solutions are established and the corresponding rates of convergence are estimated. It is also shown that the estimates obtained are close to being optimal. The proofs are based on the property of exponential mixing for the problem in question and some abstract SLLN and CLT for mixing-type Markov processes.     

非平稳φ-混合序列强律收敛速度的进一步探讨

本文研究非平稳φ 混合序列的强大数律：无需混合速度限制，给出了完全收敛成立的充要条件；在弱混合速度条件下，讨论了Ｍａｒｃｉｎｋｉｅｗｉｃｚ Ｚｙｇｍｕｎｄ强律成立的必要条件，进而得出混合情形的Ｍａｒｃｉｎｋｉｅｗｉｃｚ Ｚｙｇｍｕｎｄ强律，其结果与独立情形相一致．     

On the rate of convergence in the strong law of large numbers for martingales

The aim of this note is to establish the Baum–Katz type rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers for martingales, which improves the recent works of Stoica [Series of moderate deviation probabilities for martingales, J. Math. Anal. Appl. 336 (2005), pp. 759–763; Baum–Katz–Nagaev type results for martingales, J. Math. Anal. Appl. 336 (2007), pp. 1489–1492; A note on the rate of convergence in the strong law of large numbers for martingales, J. Math. Anal. Appl. 381 (2011), pp. 910–913]. Furthermore, we also study some relevant limit behaviours for the uniform mixing process. Under some uniform mixing conditions, the sufficient and necessary condition of the convergence of the martingale series is established.     

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.