共查询到20条相似文献,搜索用时 31 毫秒
1.
王学武 《纯粹数学与应用数学》2009,25(1):195-202
利用分析方法建立了用不等式表示的用对数似然比刻划的任意相依离散随机变量序列的强偏差定理,作为推论得到了更一般的离散随机变量序列加权和的强大数定律. 相似文献
2.
A. N. Frolov 《Journal of Mathematical Sciences》2006,133(3):1356-1370
We derive universal strong laws for increments of sums of independent, nonidentically distributed, random variables. These
results generalize universal results of the author for the i.i.d. case which include the strong law of large numbers, law
of the iterated logarithm, Erdos-Renyi law, and Csorgo-Revesz laws. Bibliography: 27 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 260–285. 相似文献
3.
利用逆鞅、截尾等方法,我们得出行-列可交换随机变量组列的大数定律,作为推论,我们得到具有有限均值的行-列可交换无限组列满足强大数定律的充要条件是该组列的对角线元素不相关.再充分利用对称性及可交换性,我们得到对称可交换随机变量和的极限定理,并由此导出对称行-列可交换随机变量组列的完全收敛定理 相似文献
4.
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
5.
Summary Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines
and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations.
Functional limit theorems for such random processes are obtained. 相似文献
6.
强大数定律的若干新结果 总被引:12,自引:0,他引:12
本文利用Hajek-Renyi型最大值不等式,获得了随机变量和的强大数定律和 收敛速度.作为应用,给出了某些相依随机变量和新的强大数定律. 相似文献
7.
随机变量序列加权和的强收敛性 总被引:12,自引:0,他引:12
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. 相似文献
8.
In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables.
Marcinkiewicz-Zygmund’s strong law of large numbers is extended to weighted sums of negatively associated random variables.
Furthermore, we investigate various limit properties of Cesàro’s and Riesz’s sums of negatively associated random variables.
Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409–412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105–112, 2000), Li et al. (J. Theor. Probab. 8, 49–76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169–178, 1993) are also improved and extended to the negatively associated setting.
相似文献
9.
NOD随机变量加权和的极限 总被引:2,自引:0,他引:2
The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5] in independent sequence case. 相似文献
10.
In this paper, we obtain theorems of complete convergence and strong laws of large numbers for weighted sums of sequences of independent random elements in a Banach space of type p (1 ≤ p ≤ 2). The results improve and extend the corresponding results on real random variables obtained by [1] and [2]. 相似文献
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12.
A. N. Frolov 《Journal of Mathematical Sciences》2005,128(1):2604-2613
We derive universal strong laws for increments of sums of i.i.d. random variables with multidimensional indices without an exponential moment. Our theorems yield the strong law of large numbers, the law of the iterated logarithm, and the Csorgo-Revesz laws for random fields. New results are obtained for distributions from domains of attraction of the normal law and of completely asymmetric stable laws with index (1, 2). Bibliography: 18 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 298, 2003, pp. 191–207. 相似文献
13.
Lixin Zhang 《中国科学A辑(英文版)》1998,41(7):736-745
Some inequalities for moments of partial sums of aB -valued strong mixing field are established and their applications to the weak and strong laws of large numbers and the complete
convergences are discussed.
Project supported by the National Natural Science Foundation of China (Grant No. 19701011) and China Postdoctoral Science
Foundation. 相似文献
14.
ABSTRACTThe asymptotic equipartition property is a basic theorem in information theory. In this paper, we study the strong law of large numbers of Markov chains in single-infinite Markovian environment on countable state space. As corollary, we obtain the strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for this process. Finally, we give the asymptotic equipartition property of Markov chains in single-infinite Markovian environment on countable state space. 相似文献
15.
Allan Gut 《Probability Theory and Related Fields》1979,46(2):205-220
Summary For a set of i.i.d. random variables indexed by the positive integer d-dimensional lattice points we give conditions for the existence of moments of the supremum of normed partial sums, thereby obtaining results related to the Kolmogorov-Marcinkiewicz strong law of large numbers and the law of the iterated logarithm. 相似文献
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We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded single-type process composed of all individuals having the same type as the ancestor. As an important intermediate step, we determine the (exact) polynomial rate of convergence of Nerman’s martingale in continuous time to its limit. The techniques used also allow us to give streamlined proofs of the weak and strong laws of large numbers and ratio convergence for the processes in focus. 相似文献
19.
Yongfeng Wu 《Journal of Mathematical Analysis and Applications》2011,377(2):613-623
Under some conditions of uniform integrability and appropriate conditions, mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables are obtained. Our results extend and improve the results of [H.S. Sung, S. Lisawadi, A. Volodin, Weak laws of large numbers for arrays under a condition of uniform integrability, J. Korean Math. Soc. 45 (2008) 289-300] and [M. Ordóñez Cabrera, A. Volodin, Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability, J. Math. Anal. Appl. 305 (2005) 644-658]. 相似文献
20.
In both the past literature and industrial practice, it was often implicitly used without any justification that the classical strong law of large numbers applies to the modeling of equity-linked insurance. However, as all policyholders’ benefits are linked to common equity indices or funds, the classical assumption of independent claims is clearly inappropriate for equity-linked insurance. In other words, the strong law of large numbers fails to apply in the classical sense. In this paper, we investigate this fundamental question regarding the validity of strong laws of large numbers for equity-linked insurance. As a result, extensions of classical laws of large numbers and central limit theorem are presented, which are shown to apply to a great variety of equity-linked insurance products. 相似文献