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1.
Relation between association and conditional association is answered, several examples show that the association of random variables does not imply the conditional association, and vice versa. Several fundamental properties of conditional associated random variables are developed, which extend the corresponding ones under the non-conditioning setup. By means of these properties, some conditional Hájek-Rényi type inequalities, a conditional strong law of large numbers and a conditional central limit theorem stated in terms of conditional characteristic functions are established, which are conditional versions of the earlier results for associated random variables, respectively. In addition, some lemmas in the context are of independent interest. 相似文献
2.
The relation between strong mixing and conditionally strong mixing is answered by examples, that is, the strong mixing property of random variables does not imply the conditionally strong mixing property, and the opposite implication is also not true. Some equivalent definitions and basic properties of conditional strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under non-conditional case. 相似文献
3.
本文研究了NA随机变量的Egorov型强大数律.利用NA随机变量的概率不等式,得到了NA随机变量序列的Egorov型强大数律的一些等价条件,所获结果推广和改进了在独立随机变量序列的Egorov的结果和在NA随机变量序列已有的一些结果. 相似文献
4.
In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob’s inequality for submartingale and Kolmogrov’s inequality. By Kolmogrov’s inequality, we obtain a special version of Kolmogrov’s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition. 相似文献
5.
For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown
to be essentially equivalent — i.e., equivalent to up to null sets. Unlike in the finite setting, a large collection of random
variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise
and multiple versions of exchangeability also follows as a corollary. Our result relies on an iterated extension of Bledsoe
and Morse's completion of the product of two measure spaces.
Part of this work was done while Peter Hammond was visiting the National University of Singapore in March–April 2004. The
final version was completed while Yeneng Sun was on sabbatical leave at the University of Illinois at Urbana–Champaign and
Stanford University in October 2004 – May 2005. 相似文献
6.
In the paper, we generalize the von Bahr–Esseen moment inequality from independent random variables to pairwise independent random variables. As the applications, the moment convergence, the complete convergence and the strong law of large numbers are established for pairwise independent random variables. 相似文献
7.
In this paper, we present a deviation inequality for a common estimator of the conditional value-at-risk for bounded random variables. The result improves a deviation inequality which is obtained by Brown [D.B. Brown, Large deviations bounds for estimating conditional value-at-risk, Operations Research Letters 35 (2007) 722-730]. 相似文献
8.
利用ρ-混合序列的Rosenthal型最大值不等式,得到了ρ-混合随机变量序列的Hájeck-Rènyi型不等式,三级数定理和Chung型强大数律,所得结果达到了独立时一致的结果. 相似文献
9.
利用随机变量的截尾方法和条件三级数定理,研究任意B值随机变量序列的极限性质,得到了一类关于条件期望的强极限定理和鞅差序列收敛定理,推广了与此相应的一些结果和若干经典的强大数定律. 相似文献
10.
11.
An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme. 相似文献
12.
本文研究了马氏环境中马氏链构成的随机变量之和的概率不等式问题.利用了结尾的方法,获得了马氏环境中马氏链构成的随机变量之和的尾部概率不等式,作为结果的应用,给出了将过程限制在(S,S∩F,PS)上的强大数定律.文中提出的方法和结果对研究独立的随机变量之和的大样本性质是十分有用的. 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.
对称随机变量序列的Hájek-Rényi型不等式和强大数律 总被引:1,自引:0,他引:1
得到了对称随机变量序列的Hájek-Rényi型不等式,并利用它研究了对称随机变量序列的强大数律. 相似文献
15.
Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima
of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some
results on strong law of large numbers are given such that our results are much stronger than the corresponding result of
Gadidov’s. 相似文献
16.
O. V. Rusakov 《Journal of Mathematical Sciences》1998,88(1):86-98
In this paper, we introduce a scheme of summation of independent random variables with random replacements. We consider a
series of double arrays of identically distributed random variables that are row-wise independent, but such that neighboring
rows contain a random common part of the repeating terms. By this-scheme we bscribe a model of strongly dependent noise. To
investigate the sample mean of this noise, we consider the sum of random variables over the whole double array and its conditional
variance with respect to replacements. For columns of the arrays we prove a covariance inequality. As a corollary of it, we
demonstrate the law of large numbers for conditional variances. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 124–143.
Translated by A. Sudakov. 相似文献
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18.
利用Utev S.和Peligrad M.不等式,得到了-混合随机变量序列的Hájeck-Rènyi不等式、三级数定理和Chung型强大数律,改进了甘师信与吴群英等人的结论,达到了与独立时一致的结果. 相似文献
19.
建立了关于AQSI序列的Kolmogorov型不等式和AQSI序列的三级数定理,讨论了AQSI序列的几乎处处收敛性并且得到了关于AQSI序列的chung型强大数定理. 相似文献
20.
Our aim is to present some limit theorems for capacities.We consider a sequence of pairwise negatively correlated random variables.We obtain laws of large numbers for upper probabilities and 2-alternating capacities,using some results in the classical probability theory and a non-additive version of Chebyshev’s inequality and Boral-Contelli lemma for capacities. 相似文献