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arXiv · 2312.07775

On the construction of stationary processes and random fields

Jeonghwa Lee
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Abstract

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.

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Jeonghwa Lee. 2023-12-12. On the construction of stationary processes and random fields. https://arxiv.org/abs/2312.07775

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