共查询到20条相似文献,搜索用时 484 毫秒
1.
M. A. Lifshits Ya. Yu. Nikitin V. V. Petrov A. Yu. Zaitsev A. A. Zinger 《Vestnik St. Petersburg University: Mathematics》2018,51(2):144-163
This is the first in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg school of probability and statistics in the period from 1947 to 2017. It is devoted to limit theorems for sums of independent random variables—a traditional subject for St. Petersburg. It refers to the classical limit theorems: the law of large numbers, the central limit theorem, and the law of the iterated logarithm, as well as important relevant problems formulated in the second half of the twentieth century. The latter include the approximation of the distributions of sums of independent variables by infinitely divisible distributions, estimation of the accuracy of strong Gaussian approximation of such sums, and the limit theorems on the weak almost sure convergence of empirical measures generated by sequences of sums of independent random variables and vectors. 相似文献
2.
The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means,which realizes the extension of the almost sure central limit theorem for partial sums from an i.i.d.sequence of random variables to a Markov chain. 相似文献
3.
Central limit theorem and almost sure central limit theorem for the product of some partial sums 总被引:1,自引:0,他引:1
Miao Yu 《Proceedings Mathematical Sciences》2008,118(2):289-294
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of
independent identically distributed random variables. 相似文献
4.
Guangyu Zou & Yong Zhang 《数学研究通讯:英文版》2012,28(4):359-366
In this paper, we prove an almost sure central limit theorem for weighted
sums of mixing sequences of random variables without stationary assumptions. We no
longer restrict to logarithmic averages, but allow rather arbitrary weight sequences.
This extends the earlier work on mixing random variables. 相似文献
5.
LiXin Zhang 《中国科学 数学(英文版)》2016,59(12):2503-2526
Kolmogorov’s exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments. For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sub-linear expectation for random variables with only finite variances. 相似文献
6.
Ferenc Móricz 《Archiv der Mathematik》2006,86(4):375-384
In recent years, the almost sure central limit theorem attracted widespread attention in Probability Theory. It involves the
harmonic (also called logarithmic) averages of a certain numerical sequence formed from a sequence of independent, identically
distributed random variables. Our primary aim is to study the convergence behavior of the sequence of harmonic averages of
a given numerical sequence from the viewpoint of Summability Theory.
Received: 12 May 2005; revised: 1 July 2005 相似文献
7.
A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
独立随机序列最大值的几乎处处极限定理 总被引:1,自引:1,他引:0
本文研究了独立随机序列最大值分布的几乎必然收敛性.利用有关协方差的不等式和加权平均,获得独立随机序列最大值的几乎处处极限.将独立同分布随机序列的结论,推广了独立但不同分布的情形. 相似文献
9.
陈佳 《高校应用数学学报(A辑)》2007,22(3):316-322
对于均值为零的平稳相伴随机变量序列,首先证明了在L(n)=EX_1~2 2 sum from n to j=2 Cov(X_1,X_j)是一个缓变函数的条件下的泛函型几乎处处中心极限定理.另外还给出了正则化部分和函数的对数平均几乎处处收敛性. 相似文献
10.
In this paper, we obtain an almost sure central limit theorem for products of independent sums of positive random variables. An extension of the result gives an ASCLT for the U-statistics. 相似文献
11.
We refine the classical Lindeberg–Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parameterized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg’s condition. This allows us to continue to provide information in nonstandard settings in which the classical central limit theorem fails to hold. Stein’s method plays a key role in the development of this theory. 相似文献
12.
Qunying Wu 《Proceedings Mathematical Sciences》2011,121(3):369-377
Consider the weight function sequences of NA random variables. This paper proves that the almost sure central limit theorem
holds for the weight function sequences of NA random variables. Our results generalize and improve those on the almost sure
central limit theorem previously obtained from the i.i.d. case to NA sequences. 相似文献
13.
ZHICHAO WENG ZUOXIANG PENG SARALEES NADARAJAH 《Proceedings Mathematical Sciences》2011,121(2):217-228
We derive under some regular conditions an almost sure local central limit theorem for the product of partial sums of a sequence
of independent identically distributed positive random variables. 相似文献
14.
Wang Zhenyuan 《Fuzzy Sets and Systems》1985,16(3):277-290
In fuzzy measure theory, as Sugeno's fuzzy measures lose additivity in general, the concept ‘almost’, which is well known in classical measure theory, splits into two different concepts, ‘almost’ and ‘pseudo-almost’. In order to replace the additivity, it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called ‘waxing’ and ‘waning’, and to introduce some new concepts, such as ‘autocontinuity’, ‘converse-autocontinuity’ and ‘pseudo-autocontinuity’. These concepts describe some asymptotic structural characteristics of a fuzzy measure.In this paper, by means of the asymptotic structural characteristics of fuzzy measure, we also give four forms of generalization for both Egoroff's theorem, Riesz's theorem and Lebesgue's theorem respectively, and prove the almost everywhere (pseudo-almost everywhere) convergence theorem, the convergence in measure (pseudo-in measure) theorem of the sequence of fuzzy integrals. In the last two theorems, the employed conditions are not only sufficient, but also necessary. 相似文献
15.
利用随机变量的截尾研究任意随机变量序列的性质,建立了一类矩条件下任意随机变量序列的强极限定理.作为推论,得到了可列非齐次马尔可夫过程的一个强极限定理,推广了鞅差序列当1≤p≤2和p≥2时的Chow定理,相应的一些已有结果和若干经典的关于独立随机变量序列的强大数定律是本文的特例。 相似文献
16.
In this paper we prove an almost sure limit theorem for random sums of independent random variables in the domain of attraction
of a p-semistable law and describe the limit law. 相似文献
17.
该文得到了关于一般可分距离空间上独立随机元序列的几乎处处中心极限定理(almost sure central limit theory, 简记为ASCLT). 作为应用, 该文给出了取值于可分Banach空间上随机元序列以及一类随机场序列满足ASCLT的充分条件,最后给出了关于多维随机变量序列极值的ASCLT. 相似文献
18.
该文讨论了非平稳负(正)相依序列加权和的几乎处处中心极限定理,改进并推广了相依序列几乎处处中心极限定理的相关结果. 相似文献
19.
Eugenijus Manstavi?ius 《Discrete Mathematics》2011,311(6):463
We deal with the random combinatorial structures called assemblies. Instead of the traditional logarithmic condition which assures asymptotic regularity of the number of components of a given order, we assume only lower and upper bounds of this number. Using the author’s analytic approach, we generalize the independent process approximation in the total variation distance of the component structure of an assembly. To evaluate the influence of strongly dependent large components, we obtain estimates of the appropriate conditional probabilities by unconditioned ones. The estimates are applied to examine additive functions defined on a new class of structures, called weakly logarithmic. Some analogs of Major’s and Feller’s theorems which concern almost sure behavior of sums of independent random variables are proved. 相似文献
20.
A. I. Martikainen 《Journal of Mathematical Sciences》2006,137(1):4549-4554
We investigate possible rates of convergence in the almost sure central limit theorem for sums of independent random variables
and martingales. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 110–119. 相似文献