In the paper, the solution of the Fokker-Planck-Kolmogorov (FPK), to of the motion of a single-degree-of-freedom (sdof) system in the linear or non-linear range under the action of a forcing function modelled by a Gaussian zero mean shot noise is approached. In previous papers a general technique for approximating the solution in the case that the restoring force had a smooth behaviour and could be modelled by a polynomial expansion was treated. In the present paper, a general approach is developed, with the help of characteristic function, allowing to apply the procedure up to any power of non-linearity. Finally, a numerical application to a highly non-linear oscillator, the dynamics of the trilite, is presented, and comparison with Monte Carlo results is discussed.
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