共查询到20条相似文献,搜索用时 31 毫秒
1.
V. V. Petrov 《Vestnik St. Petersburg University: Mathematics》2017,50(1):32-34
Sufficient conditions for the applicability of the law of the iterated logarithm to sequences of dependent random variables are obtained. As a corollary, a theorem on the law of the iterated logarithm for a sequence of m-orthogonal random variables is proved. 相似文献
2.
V. V. Petrov 《Journal of Mathematical Sciences》2003,118(6):5610-5612
Sufficient conditions are given for the applicability of the law of the iterated logarithm to a sequence of independent random variables having finite variances. Bibliography: 5 titles. 相似文献
3.
V. V. Petrov 《Journal of Mathematical Sciences》2011,176(2):207-208
New sufficient conditions are found for the applicability of the strong law of large numbers to a sequence of dependent nonnegative
random variables with finite variances. Bibliography: 4 titles. 相似文献
4.
New sufficient conditions for the applicability of the strong law of large numbers are established for sequences of random
variables without the independence conditions. Results on strong stability of sums of dependent random variables are also
obtained. No particular type of dependence between random variables of a sequence is assumed. Only conditions related to moments
of random variables and their sums are used. It is shown that the results obtained are unimprovable in certain sense. These
results are generalizations of some results of N. Etemadi proved under more restrictive conditions. 相似文献
5.
V. M. Korchevsky 《Vestnik St. Petersburg University: Mathematics》2011,44(4):268-271
New sufficient conditions for the applicability of the strong law of large numbers to a sequence of dependent random variables
X
1, X
2, …, with finite variances are established. No particular type of dependence between the random variables in the sequence
is assumed. The statement of the theorem involves the classical condition Σ
n
∞ (log2
n)2/n
2 < ∞, which appears in various theorems on the strong law of large numbers for sequences of random variables without the independence
condition. 相似文献
6.
本文利用鞅的Skorohod表示, 在序列是高斯的且序列的协方差系数以幂指数速度递减的条件下,证明了相伴高斯随机变量序列的一个强不变原理\bd 作为推论得到了相伴高斯随机变量序列的重对数律和钟重对数律 相似文献
7.
给出了具有不同分布的NA随机变量列满足的若干强大数律;作为应用,不仅将独立随机变量的一类强极限定理完整的推广到NA随机变量情形,而且关于NA随机变量的一些已有结果可以作为推论得出. 相似文献
8.
A limit of a sequence of fuzzy numbers is defined and its some properties are shown. Based on these concept and properties, an independent sequence of fuzzy random variables is considered and a strong law of large numbers for fuzzy random variables is shown. 相似文献
9.
??Examining the conditions of positively or negatively associated
sequences of random variables obeying the strong law of large numbers provided by
Alexander, the sequences of Gaussian random variables, nonnegative and uniformly bounded
sequences of random variables with general dependent structure were studied, and the
sufficient conditions for they obeying the strong law of large numbers were given. At
last, an example for Gaussian sequence satisfying the strong law of large numbers was
given. 相似文献
10.
Lutz Edler 《Statistics & probability letters》1984,2(4):203-205
The fluctuation behavior of the row sums in a triangular array of Poisson distributed random variables is described by the law of the iterated logarithm under two different assumptions of independence within the array. The results are applied to a sequence of Poisson random variables. 相似文献
11.
V. V. Petrov 《Journal of Mathematical Sciences》2003,118(6):5607-5609
Sufficient conditions are given for the applicability of the law of the iterated logarithm to sequences of independent random variables. These conditions do not include assumptions on the existence of any moments. Bibliography: 5 titles. 相似文献
12.
13.
Cheng HU 《数学年刊B辑(英文版)》2018,39(5):791-804
This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables, the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense. 相似文献
14.
B. L. S. Prakasa Rao 《Annals of the Institute of Statistical Mathematics》2009,61(2):441-460
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. 相似文献
15.
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
16.
We obtain some results concerning the upper limit of a random sequence and the law of the iterated logarithm for sums of independent random variables. 相似文献
17.
The Levy's type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables. Unfortunately, this type inequality cannot be obtained for a generalization of association, i.e., linear positive quadrant dependence, because of their special dependence structure. The purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables. 相似文献
18.
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
19.
This paper addresses the following classical question: Given a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study the question for several classes of dependent random variables. For independent and identically distributed random variables we show that the central limit theorem for the linear process is equivalent to the fact that the variables are in the domain of attraction of a normal law, answering in this way an open problem in the literature. The study is also motivated by models arising in economic applications where often the innovations have infinite variance, coefficients are not absolutely summable, and the innovations are dependent. 相似文献
20.
A. I. Martikainen 《Journal of Mathematical Sciences》1992,61(1):1879-1885
A sequence of independent random variables with zero mean generates, by applying to it the A. V. Skorokhod representation, a sequence of random arguments of a Wiener process. At the proof of limit theorems for sums of independent random variables with the use of this representation, there arises the question of the stability of the sequence of the random arguments. In the paper the law of the iterated logarithms yields exact bounds for the oscillation of this sequence.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 83–91, 1989. 相似文献