共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, a central limit theorem for strong near-epoch dependent sequences of random variables introduced in [9] is showed. Under the same moments condition, the authors essentially weaken the "size" requirement mentioned in other papers about near epoch dependence. 相似文献
2.
Lixin Zhang 《数学学报(英文版)》2000,16(4):691-710
Abstract
The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under
lower moment conditions or the Lindeberg condition. Results obtained improve a central limit theorem of Roussas [11] for negatively
assiated fields and the main results of Su and Chi [18], and also include a central limit of theorem for weakly negatively
associated random variables similar to that of Burton et al. [20].
Research supported by National Natural Science Foundation of China (No. 19701011) 相似文献
3.
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
4.
Let \(X_1,\ldots ,X_n\) be, possibly dependent, [0, 1]-valued random variables. What is a sharp upper bound on the probability that their sum is significantly larger than their mean? In the case of independent random variables, a fundamental tool for bounding such probabilities is devised by Wassily Hoeffding. In this paper, we provide a generalisation of Hoeffding’s theorem. We obtain an estimate on the aforementioned probability that is described in terms of the expectation, with respect to convex functions, of a random variable that concentrates mass on the set \(\{0,1,\ldots ,n\}\). Our main result yields concentration inequalities for several sums of dependent random variables such as sums of martingale difference sequences, sums of k-wise independent random variables, as well as for sums of arbitrary [0, 1]-valued random variables. 相似文献
5.
Summary Given a sequence of ϕ-mixing random variables not necessarily stationary, a Chernoff-Savage theorem for two-sample linear
rank statistics is proved using the Pyke-Shorack [5] approach based on weak convergence properties of empirical processes
in an extended metric. This result is a generalization of Fears and Mehra [4] in that the stationarity is not required and
that the condition imposed on the mixing numbers is substantially relaxed. A similar result is shown to hold for strong mixing
sequences under slightly stronger conditions on the mixing numbers.
Research partially supported by the National Research Council of Canada under Grant No. A-3954. 相似文献
6.
David Bartl 《Linear algebra and its applications》2012,436(9):3784-3789
We derive from Motzkin’s Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker’s Theorem of the alternative. A generalisation of the residual existence theorem for linear equations which has recently been proved by Rohn [8] is a corollary. We state all the results in the setting of a general vector space over a linearly ordered (possibly skew) field. 相似文献
7.
Somdeb Lahiri 《Journal of Applied Mathematics and Decision Sciences》2002,6(3):183-190
In this paper we provide a simple proof of the extension theorem for partial orderings due to Suzumura [1983] when the domain of the partial order is finite. The extension theorem due to Szpilrajn [1930] follows from this theorem. Szpilrajns extension theorem is used to show that an asymmetric binary relation is contained in the asymmetric part of a linear order if and only if it is acyclic. This theorem is then applied to prove three results. Finally we introduce the concept of a threshold choice function, and our third result says that such choice functions are the only ones to satisfy a property called functional acyclicity. 相似文献
8.
In this article we construct multiplicative decompositions of holomorphic Fredholm operator valued functions on Stein manifolds with values in various algebras of differential and pseudo differential operators which are submultiplicative ψ* - algebras, a concept introduced by the first author. For Fredholm functions T(z) satisfying an obvious topological condition we. Prove (0.1) T(z) = A(z)(I + S(z)), where A(z) is holomorphic and invertible and S(z) is holomorphic with values in an “arbitrarily small” operator ideal. This is a stronger condition on S(z) than in the authors' additive decomposition theorem for meromorphic inverses of holomorphic Fredholm functions [12], where the smallness of S(z) depends on the number of complex variables. The Multiplicative Decomposition theorem (0.1) sharpens the authors' Regularization theorem [11]; in case of the Band algebra L(X) of all bounded linear operators on a Band space, (0.1) has been proved by J. Letterer [20] for one complex variable and by M. 0. Zaidenberg, S. G. Krein, P. A. Kuchment and A. A. Pankov [26] for the Banach ideal of compact operators. 相似文献
9.
10.
Volker Eberhardt 《manuscripta mathematica》1971,4(3):255-262
A locally convex space E is said to be an s-space [1] if every closed linear map of E onto a barrelled space is open. The aim of this paper is to replace the B-complete spaces in the closed graph theorem of A. P. and W. ROBERTSON [7] by s-spaces. Previous work of PTAK [5] and PERSSON [4] implies that B-complete spaces and t-polar spaces are s-spaces. Thus our result includes that of ADASCH [2] who generalized Robertson's theorem, taking t-polar spaces instead of B-complete ones. 相似文献
11.
12.
E. A. Baklanov 《Siberian Mathematical Journal》2006,47(6):975-979
We prove the strong law of large numbers for the linear combinations of functions of order statistics (L-statistics) based on weakly dependent random variables. We also establish the Glivenko-Cantelli theorem for ?-mixing sequences of identically distributed random variables. 相似文献
13.
本文在文献[1]、[2]的基础上,给出并证明了非定常线性系统在经常作用干扰下稳定的充分和必要条件,并推得该系统在李雅普诺夫意义下一致渐近稳定和在经常作用干扰下稳定等价的定理.此外,作者还应用文中的定理,对机器人动态稳定性进行了比较切合实际的分析. 相似文献
14.
A coincidence theorem for a single-valued mapping in [3] is generalized as one for a strongly decomposable multivalued mapping.
Project supported by the National Natural Science Foundation of China 相似文献
15.
§ 1. Introduction ConsiderasequenceofBernoullitrials ,andsupposethatateachtrialthebettorhasthefreechoiceofwhetherornottobet.Asystemconsistsinfixedrulesselectingthosetrialsonwhichtheplayeristobet.ThetheoremongamblingsystemassertsthatunderanysystemthesuccessivebetsformasequenceofBernoullitrialwithunchangedprobabilityforsuccess.TheimportanceofthisstatementwasfirstrecognizedbyvonMises,whointroducedtheimpossibili tyofasuccessfulgamblingsystemasafundamentalaxiom(cf.[1 ],[2 ],[3],[4]) .Thecon … 相似文献
16.
Summary. Bermúdez-Moreno [5] presents a duality numerical algorithm for solving variational inequalities of the second kind. The performance
of this algorithm strongly depends on the choice of two constant parameters. Assuming a further hypothesis of the inf-sup type, we present here a convergence theorem that improves on the one presented in [5]: we prove that the convergence is linear,
and we give the expression of the asymptotic error constant and the explicit form of the optimal parameters, as a function
of some constants related to the variational inequality. Finally, we present some numerical examples that confirm the theoretical
results.
Received June 28, 1999 / Revised version received February 19, 2001 / Published online October 17, 2001 相似文献
17.
文献[1]中,我们用有关鞅的中心极限定理,证明了系统辨识中LS估计的渐近正态性。然而[1]中的条件是苛刻的。本文利用Mcleish的相依变量的中心极限定理改进了[1]的结果。 相似文献
18.
对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律. 相似文献
19.
曾唯尧 《高校应用数学学报(A辑)》1994,(3):248-255
本文我们首先推广了著名的Favard定理并指出对齐次线性概周期系统由Favard定理所得到的概周期解是平凡的。然后利用推广后的Favard定理和普通型二分性讨论了一类线性和非线性系统的概周期解存在性。Nakajima在文〔3〕中的结果是我们的结果的一种特殊情形。 相似文献
20.
田绍槐 《数学的实践与认识》2000,30(3):380-384
有限维线性定常系统的典型分解定理是控制理论的重要成果之一 [1] ,也是计算机控制的重要理论基础之一 ,本文将这一结果推广到 Hilbert空间上的无限维线性定常系统 . 相似文献