Spectral covariance and limit theorems for random fields with infinite variance

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 α-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 α-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.

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