  We prove the reduction principle for asymptotics of functionals of vector
random fields with weakly and strongly dependent components. These functionals
can be used to construct new classes of random fields with skewed and
heavy-tailed distributions. Contrary to the case of scalar long-range dependent
random fields, it is shown that the asymptotic behaviour of such functionals is
not necessarily determined by the terms at their Hermite rank. The results are
illustrated by an application to the first Minkowski functional of the Student
random fields. Some simulation studies based on the theoretical findings are
also presented.
