Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method

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.