Polynomial-Gaussian vectors and polynomial-Gaussian processes

The density of a d-dimensional polynomial-Gaussian distribution (PGDd) 5 the product of a non-negative polynomial and a Gaussian density. The density of a (PGDd) has many properties similar to a rf-dimensional Gaussian distribution (GDd), but one-dimensional marginal distributions of (PGDd) are (PGD1). Analogously one-dimensional densities of a polynomial-Gaussian process (PGP) are (PGD1). We investigate the differences and similarities between the Gaussian and non-Gaussian cases.