  This article investigates general scaling settings and limit distributions of
functionals of filtered random fields. The filters are defined by the
convolution of non-random kernels with functions of Gaussian random fields. The
case of long-range dependent fields and increasing observation windows is
studied. The obtained limit random processes are non-Gaussian. Most known
results on this topic give asymptotic processes that always exhibit
non-negative auto-correlation structures and have the self-similar parameter
$H\in(\frac{1}{2},1)$. In this work we also obtain convergence for the case
$H\in(0,\frac{1}{2})$ and show how the Hurst parameter $H$ can depend on the
shape of the observation windows. Various examples are presented.
