Moment convergence rates in the law of logarithm for moving average process under dependence

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-01-02 DOI:10.1080/17442508.2012.748057

Xiaoyong Xiao, H. Yin

引用次数: 3

Abstract

Suppose that the moving average process is based on a doubly infinite sequence of identically distributed and dependent random variables with zero mean and finite variance and that the sequence of coefficients is absolutely summable. Under suitable conditions of dependence, we show the precise rates in the law of logarithm of a kind of weighted infinite series for the first moment of the partial sums of the moving average process. This generalizes the common law of logarithm with the square root of logarithm to that with any positive power of logarithm. Moreover, we provide another law of logarithm as a supplement.

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矩收敛率在对数律下对移动平均过程的依赖

假设移动平均过程是基于一组同分布的随机变量的双无穷序列，这些随机变量均值为零，方差有限，且系数序列是绝对可和的。在适当的依赖条件下，我们给出了一类加权无穷级数的移动平均过程的部分和的第一阶矩的对数定律的精确速率。这就把对数平方根的一般规律推广到对数任意正次幂的一般规律。此外，我们还提供了另一个对数定律作为补充。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.