Many systems of practical interest are described by stochastic differential; equations excited by powers of white noise, which can be either linear or non-linear. It is shown that, in some instances of importance, these dynamics can be meaningfully analysed by means of the central limit theorem, and moreover can be reduced to models driven by the Itô stochastic differential equations. The technique is described at length for a one-dimensional system and some applications are given, for instance, for stochastic systems with multiplicative white noises. Then the simple linear oscillator excited by gaussian white noise powers is considered, and finally, the method is applied to a special class of multivariable systems. The approach is quite consistent with the maximum entropy principle.