A class of multivariate distributions related to distributions with a Gaussian component

Abstract

A class of random vectors (X,Y),X∈ℝ^j,Y∈ℝ^k with characteristic functions of the form

h(s,t)=f(s)g(t)exp{s'Ct}

where C is a (j×k)-matrix and prime stands for transposition is introduced and studied. The class contains all Gaussian vectors and possesses some of their properties. A relation of the class to random vectors with Gaussian components is of a particular interest. The problem of describing all pairs of characteristic functions f(s),g(t) such that h(s,t) is a characteristic function is open.