The Karhunen-Lo`eve expansion and the Fredholm determinant formula are used, to derive
an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of
Gaussian stationary random fields on R
d displaying long-range dependence. This distribution
reduces to the usual Rosenblatt distribution when d = 1. Several properties of this new distribution
are obtained. Specifically, its series representation, in terms of independent chi-squared
random variables, is established. Its L´evy-Khintchine representation, and membership to the
Thorin subclass of self-decomposable distributions are obtained as well. The existence and
boundedness of its probability density then follow as a direct consequence
