Estimation of evolutionary spectra for simulation of non-stationary and non-Gaussian stochastic processes

Abstract

No spectral representation-based methodology exists to simulate non-stationary and non-Gaussian stochastic processes. This is due to the inability to determine a unique evolutionary spectrum (ES) for a process with known non-stationary autocorrelation. Here, a framework is developed to estimate evolutionary spectra for non-Gaussian processes so that realizations may be simulated using spectral representation. Two cases are considered. First, the non-Gaussian ES is estimated for a process with prescribed Gaussian ES and marginal non-Gaussian probability density function (PDF). In the second case, a compatible underlying Gaussian ES is estimated for a process with incompatible prescribed non-Gaussian ES and marginal PDF.