Parametric translation models for stationary non-Gaussian processes and fields

Parametric representations, that is, deterministic functions with time and/or space argument depending on finite families of random variables, are defined and used to describe approximately stationary non-Gaussian processes and fields specified partially by their marginal distribution and second-moment properties. The proposed parametric representations are memoryless transformations of sequences of parametric stationary Gaussian processes and fields, and are referred to as parametric translation models. Conditions are established for the convergence of statistics of sequences of parametric translation models to target statistics. Two numerical examples are presented to illustrate some properties of parametric translation models and demonstrate their use in random vibration.