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Complete qth-Moment Convergence of moving average Process for m-WOD Random Variable

Wuhan University Journal of Natural Sciences 2022年第5期27卷 396-404页

作者： SONG Mingzhu WU Yongfeng CHU Ying Department of Mathematics and Computer Science Tongling UniversityTongling 244000AnhuiChina

In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random *** results in this article improve and extend the results of the moving average *** random variables include WOD,m-NA,m-NOD and mEND random variables,so the results in the paper also promote the corresponding ones in WOD,m-NA,m-NOD,m-END random variables.

关键词： m-WOD random variable moving average processes complete convergence complete qth-moment convergence

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Explicit bivariate rate functions for large deviations in AR(1)and MA(1)processes with Gaussian innovations

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Probability, Uncertainty and Quantitative Risk 2023年第2期8卷 177-212页

作者： Maicon J.Karling Artur O.Lopes Sílvia R.C.Lopes Mathematics and Statistics Institute Federal University of Rio Grande do Sul91500-900 Porto AlegreRSBrazil

We investigate the large deviations properties for centered stationary AR(1)and MA(1)processes with independent Gaussian innovations,by giving the explicit bivariate rate functions for the sequence of two-dimensional random *** the Contraction Principle,we provide the explicit rate functions for the sample mean and the sample second *** the AR(1)case,we also give the explicit rate function for the sequence of two-dimensional random vectors(W_(n))n≥2=(n^(-1(∑_(k=1)^(n)X_(k),∑_(k=1)^(n)X_(k)^(2))))_(n∈N)n≥2,but we obtain an analytic rate function that gives different values for the upper and lower bounds,depending on the evaluated set and its intersection with the respective set of exposed points.A careful analysis of the properties of a certain family of Toeplitz matrices is *** large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting,providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker *** exhibit the properties of the large deviations of the first-order empirical autocovariance,its explicit deviation function and this is also a new result.

关键词： Autoregressive processes Empirical autocovariance Large deviations moving average processes Sample moments Toeplitz matrices Yule-Walker estimator

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Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

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Wuhan University Journal of Natural Sciences 1999年第3期4卷 278-284页

作者： Deng, Ai-jiao Liu, Jing-jun

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

关键词： complete convergence almost sure convergence weighted sums, martingale differences moving average processes

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