  We propose a new method to construct a stationary process and random field
with a given convex, decreasing covariance function and any one-dimensional
marginal distribution. The result is a new class of stationary processes and
random fields. The construction method provides a simple, unified approach for
a wide range of covariance functions and any one-dimensional marginal
distributions, and it allows a new way to model dependence structures in a
stationary process/random field as its dependence structure is induced by the
correlation structure of a few disjoint sets in the support set of the marginal
distribution.

Methodology