Gaussian conditional structure of the second order and the Kagan classification of multivariate distributions

The only Kagan-n,2(loc) probability measure with Gaussian conditional structure of the second order (GCS2) is a multivariate normal distribution. Also a short review of the known results on the GCS2 distributions is given.Kagan class Gaussian conditional structure of the second order multivariate normal law linearity of regression homoscedasticity characterization