A Monte Carlo simulation model for stationary non-Gaussian processes

A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second order correlation functions than translation processes. The paper also develops an algorithm for generating samples of any non-Gaussian process in the class of mixtures of translation processes. The algorithm is based on the sampling representation theorem for stochastic processes and properties of the conditional distributions. Examples are presented to illustrate the proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes.