A class of stationary random fields with a simple correlation structure

A stationary random field is often more complicated than a univariate stationary time series, since dependence for a random field extends in all directions, while there is only the natural distinction of past and future at any instant in a univariate time series. In this paper we start from a simple correlation structure, derive a class of stationary random fields with the simple correlation function and the simple spectral density function by using linear combinations of separable spatial correlation functions, and discuss a problem of embedding a lattice model into a continuous domain model.