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Long range dependence of heavy-tailed random functions
- Part of
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- Journal:
- Journal of Applied Probability / Volume 58 / Issue 3 / September 2021
- Published online by Cambridge University Press:
- 16 September 2021, pp. 569-593
- Print publication:
- September 2021
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- Article
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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 random volatility fields and time series.
