A sample-based iterative scheme for simulating non-stationary non-Gaussian stochastic processes

Abstract

This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are first generated to satisfy target marginal distribution functions. An iterative algorithm is proposed to match the simulated covariance function of stochastic samples to the target covariance function, and only a few iterations can converge to a required accuracy. Several explicit representations, based on Karhunen-Loève expansion and Polynomial Chaos expansion, are further developed to represent the obtained stochastic samples in series forms. Proposed methods can be applied to non-stationary non-Gaussian stochastic processes, and three examples illustrate their accuracies and efficiencies.