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.