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1.
Sufficient conditions of covariance type are presented for weighted averages of random variables with arbitrary dependence structure to converge to 0, both for logarithmic and general weighting. As an application, an a.s. local limit theorem of Csáki, Földes and Révész is revisited and slightly improved. 相似文献
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For a very general weight function, the equivalent conditions of complete convergence for weighted sums of independent but
not necessary identically distributed random variables are given. The previous situation of only sufficient results except
for particular weight functions is changed. These results may help deduce many known ones and bring to light richer content.
Project supported by the National Natural Science Foundation of China (Grant No. 19671078). the Natural Science Foundation
of the Highter Education Department of Cuangdong Province and the National Science Foundation of the Education Commission
of Jiangsu Province. 相似文献
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In this paper, we study the complete convergence for weighted sums of linearly negative quadrant dependent (LNQD) random variables based on the exponential bounds. In addition, we present some complete convergence for arrays of rowwise LNQD random variables. 相似文献
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Complete convergence of weighted sums of martingale differences 总被引:2,自引:0,他引:2
Kai Fun Yu 《Journal of Theoretical Probability》1990,3(2):339-347
LetF
oF
1 ... be an increasing family of -algebras. For eachn1,X
n isF
n-measurable, andE(X
n|Fn–1) is zero almost surely, andE(|En|p|Fn–1) is bounded by a finite constant almost surely for somep2. Leta
n1,...,a
nn be constants. Conditions are given to establish the complete convergence of (a
n1
X
1+...+a
nnXn)/n
1/p
, thereby obtaining an extension of Chow's (1966) result for the case of independent and identically distributed random variables. Whenp>2, the conditions are an improvement on existing results for the case of independence and identical distribution. 相似文献
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Let X be a (real) separable Banach space, let {Vk} be a sequence of random elements in X, and let {ank} be a double array of real numbers such that limn→∞ ank = 0 for all k and Σ∞k=1 |ank| ≤ 1 for all n. Define Sn = Σnk=1 ank(Vk − EVk). The convergence of {Sn} to zero in probability is proved under conditions on the coordinates of a Schauder basis or on the dual space of X and conditions on the distributions of {Vk}. Convergence with probability one for {Sn} is proved for separable normed linear spaces which satisfy Beck's convexity condition with additional restrictions on {ank} but without distribution conditions for the random elements {Vk}. Finally, examples of arrays {ank}, spaces, and applications of these results are considered. 相似文献
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吴永锋 《纯粹数学与应用数学》2008,24(3)
在较宽泛的条件下研究了不同分布两两NQD列加权和的收敛性质,利用矩不等式和截尾方法,获得了一般双下标加权系数的加权部分和的LP收敛性和完全收敛性定理,推广了前人的相应结果. 相似文献
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设(Xni:1≤i≤n,n≥1)为行间ND阵列,g(x)是R^+上指数为α的正则变化函数,{αni:1≤i≤n,n≥1}为满足条件max1≤i≤n|ani|=0((g(n))^-1)的实数阵列.本文采用截尾的方法,得到了使ND随机变量阵列加权乘积和完全收敛的条件,并推广了以前学者的结论. 相似文献
14.
Complete convergence and almost sure convergence of weighted sums of random variables 总被引:6,自引:0,他引:6
Deli Li M. Bhaskara Rao Tiefeng Jiang Xiangchen Wang 《Journal of Theoretical Probability》1995,8(1):49-76
Letr>1. For eachn1, let {X
nk
, –<k<} be a sequence of independent real random variables. We provide some very relaxed conditions which will guarantee
for every >0. This result is used to establish some results on complete convergence for weighted sums of independent random variables. The main idea is that we devise an effetive way of combining a certain maximal inequality of Hoffmann-Jørgensen and rates of convergence in the Weak Law of Large Numbers to establish results on complete convergence of weighted sums of independent random variables. New results as well as simple new proofs of known ones illustrate the usefulness of our method in this context. We show further that this approach can be used in the study of almost sure convergence for weighted sums of independent random variables. Convergence rates in the almost sure convergence of some summability methods ofiid random variables are also established. 相似文献
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WOD随机变量加权和的完全收敛性 总被引:1,自引:0,他引:1
《高校应用数学学报(A辑)》2015,(4)
宽象限相依变量(简称WOD变量)是一类包含独立变量,负相协变量(简称NA变量),负象限相依变量(简称NOD变量)和推广的负象限相依变量(简称END变量)在内的非常广泛的相依变量.本文利用WOD变量的Rosenthal型矩不等式和随机变量的截尾技术,在一般的条件下建立了WOD变量加权和的完全收敛性.所得结果推广了若干相依变量的相应结果. 相似文献
16.
胡宏昌 《纯粹数学与应用数学》2014,(6):558-563
为了完善 AANA 序列的极限理论,利用三级数定理、Borel-Cantelli 引理及一些概率不等式,研究了AANA 随机变量序列的函数加权和。在一定的条件下,得到了其一致强收敛速度为n?13 log n,推广了关于NA随机变量序列的相应结果。 相似文献
17.
Elena Prestini 《Monatshefte für Mathematik》1988,105(3):207-216
LetfL
p(
n
),n2, be a radial function and letS
Rf be the spherical partial sums operator. We prove that if
thenS
Rf(x)f(x) a.e. asR. The result is false for
and
\frac{{2n}}{{n + 1}}$$
" align="middle" border="0">
.Partially supported by M.P.I. 相似文献
18.
A remark on almost sure convergence of weighted sums 总被引:8,自引:0,他引:8
Rolf Thrum 《Probability Theory and Related Fields》1987,75(3):425-430
Summary As a generalization of a theorem of Chow [1] it is shown by an elementary method that for i.i.d. r.v.'s X
1,...,X
n, with expectation zero and finite p-th absolute moment (p2) the weighted sums
converge to zero a.s. 相似文献
19.
We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form
where {Wnj, 1jn, n1} and {Xnj, 1jn, n1} are triangular arrays of random variables. The results obtain irrespective of the joint distributions of the random variables within each array. Applications concerning the Efron bootstrap and queueing theory are discussed. 相似文献
20.
For functions of ΛBV, we study the convergence of the partial sums of interpolating polynomials. An estimate is found for the Fourier-Lagrange coefficients of these functions. For functions in BV, convergence is shown at points of discontinuity if the order of the polynomial increases sufficiently rapidly compared to the order of the partial sum. A Dirichlet-Jordan type theorem is shown for functions of harmonic bounded variation, and this result is shown to be best possible. 相似文献