Existence and construction of translation models for stationary non-Gaussian processes

Translation models are memoryless transformations of Gaussian processes specified by their marginal distribution FF and covariance function ξξ. Iteration schemes are commonly used to find probability laws of Gaussian images of translation models, although these schemes may not converge since translation models do not exist for arbitrary functions FF and ξξ. Pairs (F,ξ)(F,ξ) for which translation models exist are said to be consistent. Optimization algorithms are developed for constructing translation models that, for consistent pairs (F,ξ)(F,ξ), match FF and ξξ, and, for inconsistent pairs (F,ξ)(F,ξ), match FF or ξξ and approximate ξξ or FF. The resulting translation models can be used in Monte Carlo simulation studies.