Long range dependence of heavy-tailed random functions

Abstract We introduce a definition of long range dependence random processes and fields on an (unbounded) index space $T\subseteq \mathbb{R}^d$ in terms integrability the covariance indicators that function exceeds any given level. This is specifically designed to cover case functions with infinite variance. show value this new its connection limit theorems via some examples including subordinated Gaussian as well volatility time series.