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1.
Almost-Sure Results for a Class of Dependent Random Variables   总被引:17,自引:0,他引:17  
The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by d + —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.  相似文献
2.
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
3.
Convergence rates of the strong law for stationary mixing sequences   总被引:8,自引:0,他引:8  
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
4.
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 and the convergence of the moments in the central limit theorem.

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The aim of this paper is to give a functional form for the central limit theorem obtained by Bradley for strong mxing sequences of random variables, under a certain assumption about the size of the maximal coefficients of correlations. The convergence of the moments of order 2 + δ in the central limit theorem for this class of random variables is also obtained.  相似文献
9.
The paper aims to establish a new sharp Burkholder-type maximal inequality in for a class of stationary sequences that includes martingale sequences, mixingales and other dependent structures. The case when the variables are bounded is also addressed, leading to an exponential inequality for a maximum of partial sums. As an application we present an invariance principle for partial sums of certain maps of Bernoulli shifts processes.

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10.
In this note we investigate the coupling of a class of dependent sequences with an independent one having the same marginal distributions. This method is then used to prove that a uniform law of averages for this class holds if a similar law holds for the associated independent sequence.  相似文献
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