Strong approximation for sums of asymptotically negatively dependent Gaussian sequences with applications

By applying the Skorohod martingale embedding method, a strong approximation theorem for partial sums of asymptotically negatively dependent (AND) Gaussian sequences, under polynomial decay rates, is established. As applications, the law of the iterated logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem for AND Gaussian sequences are derived.     

The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics

The Chung–Smirnov law of the iterated logarithm and the Finkelstein functional law of the iterated logarithm for empirical processes are used to establish new results on the central limit theorem, the law of the iterated logarithm, and the strong law of large numbers for L-statistics with certain bounded and smooth weight functions. These results are used to obtain necessary and sufficient conditions for almost sure convergence and for convergence in distribution of some well-known L-statistics and U-statistics, including Gini's mean difference statistic. A law of the logarithm for weighted sums of order statistics is also presented.     

On the law of the iterated logarithm for increments of sums of independent random variables

We obtain the law of the iterated logarithm for increments of sums of independent random variables. Our results generalize the Kolmogorov theorem and the Hartman—Wintner theorem on the law of the iterated logarithm. Bibliography: 17 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 174–186.     

Law of iterated logarithm for NA sequences with non-identical distributions

Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.     

The rate of convergence in the functional central limit theorem for random quadratic forms with some applications to the law of the iterated logarithm

We prove a convergence rate in the functional central limit theorem for quadratic forms in independent random variables satisfying a fourth moment condition. Using this result we get a law of the iterated logarithm as well as an analogue of Chung's law of the iterated logarithm for random quadratic forms.     

On the law of the iterated logarithm for sequences of dependent random variables

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.     

相伴的高斯随机变量序列的一个强不变原理

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     

一类平均算子Markov链的极限定理

该文给出了一类平均算子Ｍａｒｋｏｖ链,并证明了对此类算子Ｍａｒｋｏｖ链,其大数定理,中心极限定理及重对数定律成立。     

LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT＊

In this article,we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d.random environments.     

A finitely additive version of kolmogorov’s law of the iterated logarithm

In their paperSome finitely additive probability (to appear in Ann. Probability), Roger A. Purves and William D. Sudderth introduced the measurable strategy idea. In this paper, we first generalize the measurable strategy idea to the more general sigma-fields of subsets ofX and prove an important theorem. Then, based on this theorem, we state and prove a finitely additive version of Kolmogorov’s law of the iterated logarithm and a finitely additive version of Hartman and Wintner’s law of the iterated logarithm in a finitely additive setting. This research was written with the partial support of the U.S. Army Grant DA-ARO-D-31-124-70-G-102.     

Étude asymptotique locale de l'estimateur par ondelettesA law of the iterated logarithm for wavelet density estimator

We state a pointwise central limit theorem for the linear wavelet density estimator in a more general setting than the result of Wu [12]. Furthermore, we also give a pointwise law of the iterated logarithm for this density estimator. Our proof of the law of the iterated logarithm uses the results of Mason [9] on the asymptotic behavior of the tail empirical process. To cite this article: A. Massiani, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 553–556.     

Strassen定理的一个推广

该文得到了在(p,r) -容度及 Holder 范数意义下的Schilder 定理. 作为它的一个应用, 作者在此情形下证明了一个更强的Strassen 重对数律.     

Convergence en loi et lois du logarithme itéré pour les vecteurs gaussiens

In this paper we prove a Strassen version of the law of the iterated logarithm for some sequences of weakly asymptotically independant Banach space valued gaussian random variables which converge in distribution, and we prove that the central limit theorem implies the functional form of the law of the iterated logarithm for the partial sums of certain Banach space valued gaussian sequences.Furthermore we give conditions for the convergence in distribution of sequences of gaussian random variables and gaussian stochastic processes, and these conditions permit us to prove that our results generalize in the gaussian case all similar results known to the authors at present.     

A Berry-Esseen Theorem and a Law of the Iterated Logarithm for Asymptotically Negatively Associated Sequences

Negatively associated sequences have been studied extensively in recent years, Asymptotically negative association is a generalization of negative association, In this paper a Berry Esseen theorem and a law of the iterated logarithm are obtained for asymptotically negatively associated sequences.     

On the law of the iterated logarithm in multiserver open queueing networks

The paper is devoted to the analysis of queueing systems in the context of the network and communication theory. We investigate a theorem on the law of the iterated logarithm for a queue of jobs in a multiserver open queueing network under heavy traffic conditions.     

The law of the iterated logarithm in C[0,1]

The law of the iterated logarithm is proved for C[0,1] valued random variables under conditions related to those used to establish the central limit theorem.Supported in part by NSF Grant GP 18759.     

A functional law of the iterated logarithm for associated sequences

Recently, a functional central limit theorem and a Berry-Essen Theorem have been demonstrated for classes or associated random variables. Using these results, and similar results for multiplicative sequences, we show a functional law of the iterated logarithm for associated sequences satisfying a rate requirement.     

CONVERGENCE OF THE CLIPPED SAMPLE AUTOCORRELATION AND AUTOCOVARIANCE

1.IntroductionClassicalmethodstoestimatetheautocorrelationandautocovarianceofastationarylineartimeseriesworkwellforgoodobservations,buttheyaresensitivetotheexistenceofoutliers.[1]gayeamethodofestimatinganARprocessbycountingthenumberofcertainrunsintheassociatedclippedbinaryseries.Althoughinsodoingsomeefficiencyislost,theproceduregivesgoodestimatesagainstoutliers.LetX.,n=0,11,12,'1beareallinearGaussiansequencewithzeromeanandautocorrelationspj~EXoXj/EXI,j=0,1,'landXu,n~0,11,',theclipped…     

有限级亚纯函数的不变原理

研究有限级亚纯函数的统计性质,证明了有限级亚纯函数的几乎必然不变原理,如中心极限定理、重对数定律和泛函中心极限定理等统计定律是几乎必然不变原理的推论.     

Radial growth of Bloch functions in the complex ball

We show that N.G. Makarov’s law of the iterated logarithm governs the radial growth of weighted Bloch functions in the complex unit ball. The argument is based on an analog of M. Weiss’ theorem for special lacunary series in the ball.