Simulation of non-Gaussian processes using fractile correlation

Abstract

The difficulties of simulating non-Gaussian stochastic processes to follow arbitrary product-moment covariance models and arbitrary non-Gaussian marginal distributions are well known. This paper proposes to circumvent these difficulties by prescribing a fractile correlation function, rather than the usual product-moment covariance function. This fractile correlation can be related to the product-moment correlation of a Gaussian process analytically. A Gaussian process with the requisite product-moment correlation can be simulated using the Karhunen-Loeve (K-L) expansion and transformed to satisfy any arbitrary marginal distribution using the usual CDF mapping. The fractile correlation of the non-Gaussian process will be identical to that of the underlying Gaussian process because it is invariant to monotone transforms. This permits the K-L expansion to be extended in a very general way to any second-order non-Gaussian processes. The simplicity of the proposed approach is illustrated numerically using a stationary squared exponential and a non-stationary Brown-Bridge fractile correlation function in conjunction with a shifted lognormal and a shifted exponential marginal distribution. © 2003 Elsevier Ltd. All rights reserved.