Generalized hermite analysis of nonlinear stochastic systems

By means of a generalized Hermite analysis we investigate nonlinear oscillator systems driven by white noise excitations. Nonstationary solutions of associated Fokker-Planck equations can be expanded by orthonormal polynomials which are generated if the Gaussian weighting function of the classical Hermite polynomials is replaced by stationary density distributions of the diffusion equation. In particular, this method is applied to calculate correlation functions and power spectra for the stochastic Duffing oscillator and for nondifferentiable restoring forces with backlash.