共查询到20条相似文献,搜索用时 31 毫秒
1.
T. Mikosch 《Monatshefte für Mathematik》1989,107(2):137-153
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. 相似文献
2.
3.
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
4.
A. N. Frolov 《Journal of Mathematical Sciences》2006,137(1):4575-4582
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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 174–186. 相似文献
5.
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
6.
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
7.
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. 相似文献
8.
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes. 相似文献
9.
Pingyan Chen 《随机分析与应用》2013,31(1):89-103
Abstract This article considers the partial sums from a sequence of independent and identically distributed random variables. It is well-known that the Hartman-Wintner law of the iterated logarithm holds if and only if the second moment exists. This article studies the generalized law of the iterated logarithm for the partial sums when they are normalized by a sequence of constants that are regularly varying with index 1/2. As a result, two equivalent conditions for the law are obtained. 相似文献
10.
Ukrainian Mathematical Journal - We obtain asymptotic estimates in the law of iterated logarithm for the extreme values of a sequence of independent random variables in Banach spaces. 相似文献
11.
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. 相似文献
12.
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
13.
T. Mikosch 《Monatshefte für Mathematik》1988,106(1):25-40
In this paper we prove bounded laws of the iterated logarithm for Gaussian quadratic forms. The underlying sequence of Gaussian variables is assumed to satisfy quite general conditions on its covariance structure. Basic tools are maximal inequalities of exponential type for sums of dependent random variables which may be of own interest. Several examples illustrate the sharpness of the results. In a particular section the bounded law of the iterated logarithm is shown for quadratic variation of Brownian motion. 相似文献
14.
We consider a partial-sum process generated by a sequence of nonidentically distributed independent random variables. Assuming
that this process is available for observation along an arbitrary time sequence, we fill the gaps by linear interpolation
and prove the functional law of the iterated logarithm (FLIL) for sample paths obtained in this way. Assuming that the V.
A. Egorov condition holds, we show that FLIL is valid, while under other conditions sufficient for the usual law of the iterated
logarithm FLIL may fail. Bibliography: 16 titles.
Translated, fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 73–95. 相似文献
15.
NA随机变量是一包含独立随机变量在内的有广泛应用的随机变量类,本文在一些更弱的条件下,建立了具有不同分布NA随机变量列的强大数律和有界重对数律,进而推广了已有的关于NA随机变量的结果。 相似文献
16.
J. Kuelbs 《Probability Theory and Related Fields》1976,33(4):221-235
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. 相似文献
17.
Uwe Einmahl 《Probability Theory and Related Fields》1989,82(2):213-223
Summary Kuelbs (1975) established a Kolmogorov-Erdös-Petrowski type integral test for lower and upper classes in the law of the iterated logarithm for sums of i.i.d. Hilbert space valued Gaussian mean zero random variables. We show that this integral test remains valid for sums of i.i.d. pregaussian mean zero random variables satisfying an additional (very mild) assumption. 相似文献
18.
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
19.
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
20.
O. Sh. Sharipov 《Lithuanian Mathematical Journal》2009,49(2):203-215
Under optimal moment conditions, we prove the compact law of the iterated logarithm and the almost sure invariance principle
for ψ-mixing random variables with values in type 2 Banach spaces. These results, together with the bounded law of the iterated
logarithm proved earlier by author, allow us to prove the same kind of results for the Banach space valued autoregressive
processes with ψ-mixing innovations. The results for autoregressive processes can be considered as asymptotic properties of the estimator
of mean. 相似文献