共查询到20条相似文献,搜索用时 31 毫秒
1.
G. Krupa 《Set-Valued Analysis》2000,8(3):237-251
We present the Komlós theorem for multivalued functions whose values are closed (possibly unbounded) convex subsets of a separable Banach space. Komlós theorem can be seen as a generalization of the SLLN for it deals with a sequence of integrable multivalued functions that do not have to be identically distributed nor independent. The Artstein–Hart SLLN for random sets with values in Euclidean spaces is derived from the main result. Finally, since the main theorem concerns multifunctions whose values are allowed to be unbounded, we can restate it in terms of normal integrands (random lower semicontinuous functions). 相似文献
2.
Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications 下载免费PDF全文
In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive. 相似文献
3.
Henry Teicher 《Journal of Theoretical Probability》1998,11(4):979-995
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. 相似文献
4.
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
5.
设{X,Xn,n≥0}是两两独立同分布的随机变量序列,1
1.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. 相似文献
6.
Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under a
framework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application 相似文献
7.
8.
In 1952 Darling proved the limit theorem for the sums of independent identically distributed random variables without power moments under the functional normalization. This paper contains an alternative proof of Darling’s theorem, using the Laplace transform. Moreover, the asymptotic behavior of probabilities of large deviations is studied in the pattern under consideration. 相似文献
9.
10.
We obtain the distribution of the sum of independent Mittag–Leffler (ML) random variables which are not necessarily identically distributed. Firstly we discuss the corresponding known result for independent and identically distributed ML random variables which follows as a special case of our result. Some applications of the obtained result to fractional point processes are also discussed. 相似文献
11.
对于独立同分布随机变量序列{Xn,n≥1},证明了其满足弱大数律的一个必要条件是:对于任何r∈(0,1),E|X|r<∞都成立.另外我们还举例说明了这样的条件不是充分的. 相似文献
12.
Malay Ghosh Gutti Jogesh Babu Nitis Mukhopadhyay 《Probability Theory and Related Fields》1975,33(1):49-54
For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables. 相似文献
13.
H. Walk 《Archiv der Mathematik》2007,89(5):466-480
For a sequence of real random variables C
α-summability is shown under conditions on the variances of weighted sums, comprehending and sharpening strong laws of large
numbers (SLLN) of Rademacher-Menchoff and Cramér-Leadbetter, respectively. Further an analogue of Kolmogorov’s criterion for
the SLNN is established for E
α-summability under moment and multiplicativity conditions of 4th order, which allows one to weaken Chow’s independence assumption
for identically distributed square integrable random variables. The simple tool is a composition of Cesàro-type and of Euler
summability methods, respectively.
Received: 12 June 2006, Revised: 14 May 2007 相似文献
14.
Lajos Horváth 《Statistics & probability letters》1985,3(4):221-225
This note represents a probability inequality for an approximation of Abel sums of independent, identically distributed random variables. This approximation implies a rate for the Prohorov-Lévy distance between Abel sums and their limit process. 相似文献
15.
LiXin Zhang 《中国科学 数学(英文版)》2016,59(4):751-768
Classical Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng (2008), we introduce the concept of negative dependence of random variables and establish Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations. As an application, we show that Kolmogorov’s strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite. 相似文献
16.
本文得到次线性期望下独立同分布的随机变量的样本轨道大偏差. 在次线性期望下所得的结果推广了概率空间的相应结果. 相似文献
17.
18.
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
19.
B. Meredov 《Ukrainian Mathematical Journal》1991,43(1):117-121
There are proved limit theorems for random processes constructed from sums of independent identically distributed random variables.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 141–145, January, 1991. 相似文献
20.
In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison's weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended. 相似文献