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

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-Loeve 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. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces a new numerical scheme for simulating stochastic processes based on their specified marginal distribution functions and covariance functions. By generating stochastic samples to meet target marginal distribution functions and using an iterative algorithm to match the simulated covariance function to the target, the proposed method can accurately represent stochastic samples in series forms. The approach is applicable to non-stationary non-Gaussian stochastic processes and is demonstrated through three examples to be accurate and efficient.