Nonlinear systems, driven by external white noise input processes and
handled by means of pseudo-force theory, are transformed through simpl
e coordinate transformation to quasi-linear systems. By means of Ito s
tochastic differential calculus for parametric processes, a finite hie
rarchy for the moment equations of these systems can be exactly obtain
ed. Applications of this procedure to the first-order differential equ
ation with cubic nonlinearity and to the Duffing oscillator show the v
ersatility of the proposed method. The accuracy of the proposed proced
ure improves by making use of the classical equivalent linearization t
echnique.