# Long range dependence of heavy-tailed random functions

@article{Kulik2021LongRD,
title={Long range dependence of heavy-tailed random functions},
author={Rafal Kulik and E. Spodarev},
journal={Journal of Applied Probability},
year={2021},
volume={58},
pages={569 - 593}
}
• Published 2 June 2017
• Mathematics
• Journal of Applied Probability
Abstract We introduce a definition of long range dependence of random processes and fields on an (unbounded) index space $T\subseteq \mathbb{R}^d$ in terms of integrability of the covariance of indicators that a random function exceeds any given level. This definition is specifically designed to cover the case of random functions with infinite variance. We show the value of this new definition and its connection to limit theorems via some examples including subordinated Gaussian as well as…
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