Simulating Non-Gaussian Stationary Stochastic Processes by Translation Model

The translation model is a useful tool to characterize stochastic processes or random fields. In this paper, this model is extended to simulate stochastic processes with discrete marginal distributions. A theoretical discussion is elaborated on the properties of the correlation distortion function. The spectral representation method is employed to generate the underlying Gaussian process of the translation model. Efficient algorithms are developed to determine the power spectral density function (PSDF) Sz(omega) for Gaussian process. If the marginal distribution and PSDF of the target stochastic process are incompatible, two methods are presented to modify Sz(omega). Finally, numerical examples are performed to check the proposed methods.