The crucial problem in non-linear stochastic adaptive systems via the certainly equivalence principle is the estimation of the disturbances, which is essentially a non-linear estimation. The present paper focuses mainly on this aspect of adaptation, and the basic idea is of using the maximum entropy principle together with constraints suitably chosen. In this way one proposes a new technique for solving the Fokker-Plank-Kolmogorov equation and two new techniques for determining the conditional probability density of a random disturbance in a stochastic process. Then an adiabatic elimination is proposed, which applies when the system is slowly varying with respect to the external parameter. Finally, one shows how the dynamic equations of the state moments, combined with a linearization technique, can be utilized to analyse a broad class of non-linear stochastic systems involving random disturbances with small variances.