Asymptotic of spectral covariance for linear random fields with infinite variance

Abstract

In the paper we continue to investigate measures of dependence for random variables with infinite variance. The asymptotic of spectral covariance $\rho (X_{(0,0)},X_{(k_1,k_2)})$ for linear random field $X_{k,l}={\sum }_{i,j=0}^{\infty }{c}_{i,j}{\epsilon }_{k-i,l-j},(k,l)\in {\mathbb{Z}}^2,$ with special form of filter $\{c_{i,j}\}$ and with innovations $\{{\epsilon }_{i,j}\}$ having infinite second moment is investigated. Different behavior of $\rho (X_{(0,0)},X_{(k_1,k_2)})$ is obtained in the cases $n\to \infty ,m\to \infty$ and $n\to \infty ,m\to -\infty$, the latter case being much more complicated.

References in corpus (1)

• On $\alpha$-covariance, long, short and negative memories for sequences of random variables with infinite variance

Cited by in corpus (1)

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