共查询到20条相似文献,搜索用时 46 毫秒
1.
Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables 总被引:15,自引:0,他引:15
The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences. 相似文献
2.
We introduce a new class of dependent sequences of random variables, which is a subclass of near-epoch dependent sequences,
but can also be approximated by mixing sequences. For this kind of sequences of random variables, we call them strong near-epoch
dependent sequences, ap-order,p > 2, (maximum) moment inequality is established under weaker dependence sizes. 相似文献
3.
4.
Richard C Bradley 《Journal of multivariate analysis》1981,11(1):1-16
This article is motivated by a central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations. Here we show that the mixing condition can be weakened slightly, and construct a class of stationary random sequences covered by the new version of the theorem but not Ibragimov's original version. Ibragimov's theorem is also extended to triangular arrays of random variables, and this is applied to some kernel-type estimates of probability density. 相似文献
5.
Partially exchangeable sequences representable as mixtures of Markov chains are completely specified by de Finetti’s mixing measure. The paper characterizes, in terms of a subclass of hidden Markov models, the partially exchangeable sequences with mixing measure concentrated on a countable set, for sequences of random variables both on a discrete space and on a Polish space. 相似文献
6.
Magda Peligrad 《Journal of Theoretical Probability》1996,9(3):703-715
The aim of this paper is to investigate the asymptotic normality for strong mixing sequences of random variables in the absense of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences. The class of applications include filters of certain Gaussian sequences.Supported in part by an NSF grant, cost-sharing from the University of Cincinnati, and a Taft research grant. 相似文献
7.
We consider the bounded and compact laws of the iterated logarithm for weakly dependent Hilbert space valued random variables. Under optimal moment conditions, we prove the bounded and compact laws of the iterated logarithm for sequences of identically distributed Hilbert space valued random variables satisfying the uniform strong mixing condition. 相似文献
8.
冯凤香 《纯粹数学与应用数学》2010,26(4):570-575
利用矩不等式和截尾的方法,讨论了不同分布的φ混合序列的最大值不等式.作为应用,获得了混合序列的一阶矩及p(p〉1)阶矩分别存在有限的充分条件,这是一个与独立同分布情形一致的结果. 相似文献
9.
随机环境中纯生过程的一个极限性质 总被引:1,自引:0,他引:1
本文证明了随机环境中纯生过程的一个强极限性质,假设环境为一混合序列,不必平稳,且具有有限均值,混合系数由环境序列中一对随机变量而定。 相似文献
10.
11.
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
12.
Zbigniew S. Szewczak 《Journal of multivariate analysis》2001,78(2):64
For a nonnegative strictly stationary random sequence satisfying the “minimal” dependence condition necessary and sufficient conditions for the relative stability are found. As an application the well-known Khinchine stability result for i.i.d. random variables is proved for uniformly strong mixing sequences. 相似文献
13.
Margarida Brito Ana Cristina Moreira Freitas 《Statistics & probability letters》2010,80(23-24):1835-1843
We consider the estimation of the tail-index for dependent random variables. We establish the consistency of the geometric-type estimator (Brito and Freitas, 2003) for stationary sequences satisfying general mixing conditions and derive a simplified condition, specially adapted for applications. 相似文献
14.
15.
Florence Merlevède 《Stochastic Processes and their Applications》2012,122(1):386-417
In this paper, we obtain precise rates of convergence in the strong invariance principle for stationary sequences of real-valued random variables satisfying weak dependence conditions including strong mixing in the sense of Rosenblatt (1956) [30] as a special case. Applications to unbounded functions of intermittent maps are given. 相似文献
16.
本文研究了混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了混合序列部分和的收敛性,并进一步得到了混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果. 相似文献
17.
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met (an “infinitesimality” assumption, and a restriction to “full” distributions), the possible limit distributions are precisely the operator-self-decomposable laws. 相似文献
18.
该文引入了混合阵列的概念,讨论了混合阵列的完全收敛性与依概率收敛性.所得结果,推广了行独立随机变量阵列相应的结果.此外还得到了一般随机变量阵列的完全收敛性与依概率收敛性. 相似文献
19.
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
20.
Magda Peligrad 《Probability Theory and Related Fields》1985,70(2):307-314
Summary In this note we estimate the rate of convergence in Marcinkiewicz-Zygmung strong law, for partial sumsS
n
of strong stationary mixing sequences of random variables. The results improve the corresponding ones obtained by Tze Leung
Lai (1977) and Christian Hipp (1979). 相似文献