A new numerical scheme for simulating non-gaussian and non-stationary stochastic processes

TL;DR

This paper introduces a novel numerical scheme for efficiently simulating non-Gaussian, non-stationary stochastic processes by generating samples with specified distributions and covariances, using iterative and series expansion methods.

Contribution

The paper develops a new iterative algorithm combined with explicit series representations to accurately simulate complex stochastic processes with specified marginal and covariance functions.

Findings

The method accurately matches target covariance functions with few iterations.

Series expansions effectively represent the stochastic samples.

Examples demonstrate high accuracy and efficiency of the proposed scheme.

Abstract

This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically 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 times iterations can converge to a required accuracy. Several explicit representations, based on Karhunen-Lo\`{e}ve expansion and Polynomial Chaos expansion, are further developed to represent the obtained stochastic samples in series forms. Proposed methods can be applied to non-gaussian and non-stationary stochastic processes, and three examples illustrate their accuracies and efficiencies.