On a characterization of processes by the independence of linear forms in a triangular system

Necessary and sufficient conditions are given for a stochastic process to be either a Gaussian or an independent increments process. These conditions are based on the independence of some linear forms in a triangular system and the linearity of regression. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.