$\chi ^2$ Random Fields in Space and Time

This paper introduces some χ ² random functions, which are not homogeneous (stationary) in general, but contain the stationary case as a special case, and whose correlation structures are nonparametric and flexible so that many parametric forms can be specified. The mean square differentiability of such χ ² random function is discussed. We also make the comparison of two χ ² random functions through their finite-dimensional Laplace transforms.