Spectral covariance and limit theorems for random fields with infinite variance

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• 作者：Julius Damarackas ; Vygantas Paulauskas ; ^{vygantas.paulauskas@mif.vu.lt}
• 关键词：primary ; 60E07 ; secondary ; 62G52 ; 60G60
• 刊名：Journal of Multivariate Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：153
• 期：Complete
• 页码：156-175
• 全文大小：553 K
• 卷排序：153

文摘

In the paper, we continue to investigate measures of dependence for random variables with infinite variance. For random variables with regularly varying tails, we introduce a general class of such measures, which includes the codifference and the spectral covariance. In particular, we investigate the αα-spectral covariance, a new measure from this general class, for linear random fields with infinite second moment. Under some conditions on the filter of a linear random field, we investigate asymptotic properties of the αα-spectral covariance for linear random fields with infinite variance. We also provide an application of spectral covariances for limit theorems for stationary and associated random fields with infinite variance.