TITLE: Wiener-Hermite functional representation of nonlinear
AUTHOR: Roy-R-Valery. Spanos-Pol-D.
INSTITUTION: Rice Univ, Houston, TX, USA.
SOURCE: Structural Safety v 6 n 2-4 Nov 1989. p 187-202.
PUBLICATION: JA (Journal Article).
ABSTRACT: In this paper functionals of the vector Wiener process W(t)
are defined, from the perspective of representing the
response of nonlinear stochastic systems described by Ito
stochastic differential equations. Wiener kernels are found
in closed form for the class of bilinear systems. The
general case of nonlinear, analytic systems is studied
through the use of Carleman linearization process, whereby
the original system is converted into a bilinear one of
infinite dimension. Wiener kernels and transfer functions
are found by the application of a perturbation method. The
case of the Duffing oscillator is studied, and the results
obtained by the present analytical technique are compared
with those obtained by Gaussian closure and digital
simulations. (Author abstract) 22 Refs.