# Long range dependence of heavy tailed random functions

## TL;DR

This paper proposes a new definition of long-range dependence for heavy-tailed random functions, extending classical concepts to infinite variance cases and demonstrating its relevance through examples and limit theorems.

## Contribution

It introduces a novel, integrability-based definition of long-range dependence applicable to infinite variance processes, linking it to limit theorems and broadening the understanding of dependence in heavy-tailed fields.

## Key findings

- New definition captures long-range dependence in infinite variance processes
- Application to subordinated Gaussian and volatility fields
- Connections established with limit theorems

## Abstract

We introduce a definition of long range dependence of random processes and fields on an (unbounded) index space $T\subseteq \R^d$ in terms of integrability of the covariance of indicators that a random function exceeds any given level. This definition is particularly 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 on some examples including subordinated Gaussian as well as random volatility fields and time series.