A CLASS OF NON-GAUSSIAN PROCESSES FOR MONTE CARLO SIMULATION

Abstract

A new model is proposed to represent non-Gaussian stationary processes and develop Monte Carlo simulation algorithms for generating sample paths of non-Gaussian processes. The model is based on a class of non-Gaussian processes, the class of conditional Gaussian processes. Two representations are considered for these processes. The first representation is based on a randomized version of the classical spectral density function. The second representation uses the output of a linear filter with random coefficients subjected to Gaussian noise to define conditional Gaussian processes. The proposed model, its representations, and corresponding Monte Carlo simulation algorithms are illustrated by examples involving non-Gaussian random variables and processes. It is shown that the proposed model can match any second moment properties but, generally, can only fit approximately a specified marginal distribution.