{"title":"Moment convergence rates in the law of logarithm for moving average process under dependence","authors":"Xiaoyong Xiao, H. Yin","doi":"10.1080/17442508.2012.748057","DOIUrl":null,"url":null,"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.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics-An International Journal of Probability and Stochastic Processes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2012.748057","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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