APPLICATION OF THE WIENER HERMITE FUNCTIONAL METHOD TO THE STOCHASTIC OSCILLATOR

The Wiener Hermite functional (WHF) method is applied to the stochastic oscillator model under stable system conditions. The application concerns a non-linear trivariate-input/single-output problem. Gaussian random noise sources are assumed. A set of coupled integral equations is established in the frequency domain for any required approximation accuracy (WHF N approximation), from which noise signature functions of the response can be derived. The oscillator model is explicitly treated in a second-order approximation (WHF-2 approximation) with white noise sources and the resulting steady-state value and the power spectral density of the response are compared with exact results derived by the Fokker-Planck method. The approximative results exhibit the same structure as recently found in the application of the WHF method to point reactor kinetics driven by random reactivity fluctuations.