  We propose a new method to construct a stationary process and random field
with a given decreasing covariance function and any one-dimensional marginal
distribution. The result is a new class of stationary processes and random
fields. The construction method utilizes a correlated binary sequence, and it
allows a simple and practical way to model dependence structures in a
stationary process and 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. Simulation results of the proposed models are provided,
which show the empirical behavior of a sample path.
