SIMULATION OF STATIONARY NON-GAUSSIAN TRANSLATION PROCESSES

A simulation algorithm is developed for generating realizations of non -Gaussian stationary translation processes X(t) with a specified margi nal distribution and covariance function. Translation processes are me moryless nonlinear transformations X(t) = g[Y(t)] of stationary Gaussi an processes Y(t). The proposed simulation algorithm has three steps. First, the memoryless nonlinear transformation g and the covariance fu nction of Y(t) need to be determined from the condition that the margi nal distribution and the covariance functions of X(t) coincide with sp ecified target functions. It is shown that there is a transformation g giving the target marginal distribution for X(t). However, it is not always possible to find a covariance function of Y(t) yielding the tar get covariance function for X(t). Second, realizations of Y(t) have to be generated. Any algorithm for generating samples of Gaussian proces ses can be used to produce samples of Y(t). Third, samples of X(t) can be obtained from samples of Y(t) and the mapping of X(t) = g[Y(t)]. T he proposed simulation algorithm is demonstrated by several examples, including the case of a non-Gaussian translation random field.