On Properties and Applications of Gaussian Subordinated Lévy Fields

Robin Merkle () and Andrea Barth ()
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Robin Merkle: University of Stuttgart
Andrea Barth: University of Stuttgart

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 2, 1-33

Abstract: Abstract We consider Gaussian subordinated Lévy fields (GSLFs) that arise by subordinating Lévy processes with positive transformations of Gaussian random fields on some spatial domain. The resulting random fields are distributionally flexible and have in general discontinuous sample paths. Theoretical investigations of the random fields include pointwise distributions, possible approximations and their covariance function. As an application, a random elliptic PDE is considered, where the constructed random fields occur in the diffusion coefficient. Further, we present various numerical examples to illustrate our theoretical findings.

Keywords: Subordination; Lévy fields; Pointwise distribution; Covariance function; Random elliptic PDEs; 60G15; 60E07; 60G60; 60E10; 35R60 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10033-2

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