In this paper, the stochastic Wiener Hermite expansion (WHE) is used to find the statistical
measures (mean and variance) of the first order stochastic approximation (Gaussian part) of
the stochastic solution processes related to the nonlinear damped Duffing oscillator model which is
excited randomly by white noise process. Under the application of WHE, a deterministic model is
generated to simulate the statistical measures. In next stages, smi-analytical treatments are performed
under applying multi-step differential transformed method (Ms-DTM) and some cases study are illustrated
related to the statistical properties using Mathematica10 software.