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.

翻译：本文提出了一种构建具有给定递减协方差函数及任意一维边缘分布的平稳过程与随机场的新方法。该结果构成了一类新的平稳过程与随机场。此构建方法利用相关二元序列，为平稳过程与随机场中的依赖结构建模提供了一种简单实用的途径——其依赖结构由边缘分布支撑集中若干不相交集合的相关结构所诱导。文中给出了所提模型的仿真结果，展示了样本路径的经验行为。