On the construction of stationary processes and random fields

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, an...

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Bibliographic Details
Published inDependence modeling Vol. 12; no. 1; pp. 501 - 520
Main Author Lee, Jeonghwa
Format Journal Article
LanguageEnglish
Published De Gruyter 31.07.2024
Subjects
60G60
generalized Bernoulli process
Primary 60G10
random fields
stationary processes
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Summary: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.
ISSN:2300-2298
2300-2298
DOI:10.1515/demo-2024-0005