Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in $R^2$ with non--zero mean

Michael B. Marcus, Jay Rosen

Let $G=(G_1,G_2)$ be a Gaussian vector in $R^2$ with $E{G}_1{G}_2\ne 0$. Let $c_1,c_2\in R^1$. A necessary and sufficient condition for $G=((G_{1}+c_{1}α)^{2},(G_{2}+c…