  The paper studies the asymptotic behaviour of weighted functionals of
long-range dependent data over increasing observation windows. Various
important statistics, including sample means, high order moments, occupation
measures can be given by these functionals. It is shown that in the discrete
sampling case additive functionals have the same asymptotic distribution as the
corresponding integral functionals for the continuous functional data case.
These results are applied to obtain non-central limit theorems for weighted
additive functionals of random fields. As the majority of known results concern
the discrete sampling case the developed methodology helps in translating these
results to functional data without deriving them again. Numerical studies
suggest that the theoretical findings are valid for wider classes of long-range
dependent data.
