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.

翻译：我们提出了一种构造具有给定凸递减协方差函数和任意一维边缘分布的平稳过程与随机场的新方法。由此得到了一类新的平稳过程与随机场。该构造方法为广泛的协方差函数和任意一维边缘分布提供了一种简单、统一的技术路径，并开创了在平稳过程/随机场中建模依赖结构的新方式——其依赖关系由边缘分布支撑集中少数不相交集的相关结构所诱导。