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 marginal distribution and covariance function. Translation processes are memoryless nonlinear transformations X(t) = g[Y(t)] of stationary Gaussian processes Y(t). The proposed simulation algorithm has three steps. First, the memoryless nonlinear transformation g and the covariance function of Y(t) need to be determined from the condition that the marginal distribution and the covariance functions of X(t) coincide with specified 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 target covariance function for X(t). Second, realizations of Y(t) have to be generated. Any algorithm for generating samples of Gaussian processes 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)]. The proposed simulation algorithm is demonstrated by several examples, including the case of a non-Gaussian translation random field.