Simulation of Non-Gaussian Stochastic Processes with Nonlinear Filters

Abstract

Nonlinear filters are designed to generate stationary stochastic processes with the knowledge of their spectral densities and first-order probability densities. Two types of spectral densities are considered: the low-pass type and the narrow-band type. In particular, the nonlinear filters are represented in the form of Itô stochastic differential equations, in which the drift coefficients are adjusted to match the spectral density, and the diffusion coefficients are determined according to the probability distribution. The scheme can be used to generate excitation random processes which are clearly non-Gaussian. Since such excitations are described by stochastic differential equations, they can be combined with the governing equations of the excited dynamical systems in analytical investigation, or as a basis for Monte Carlo simulation.