Generating Laplace process with desired autocorrelation from Gaussian AR processes

Abstract

In this paper, we show a convenient way of generating a Laplace process of a desired autocorrelation. Our approach is based upon the fact that the real or imaginary component of the product of two independent complex Gaussian random variables has a Laplace marginal probability density function (pdf). We, therefore, generate a Laplace process by multiplying two independent complex Gaussian autoregressive (AR) processes. By establishing the relationship of the autocorrelation of the complex Gaussian AR processes with the autocorrelation of the resulting Laplace process, we show a convenient and simple method of selecting the parameters of the Gaussian AR processes to obtain desired autocorrelation values of the Laplace Process. To verify the method, we provide computer simulations of generating Laplace processes by the method using illustrative examples and compare their statistical characteristics to theoretical values.