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.
%0 Journal Article
%1 merkle2023properties
%A Merkle, Robin
%A Barth, Andrea
%D 2023
%I Springer
%J Methodology and Computing in Applied Probability
%K
%P 62
%R 10.1007/s11009-023-10033-2
%T On Properties and Applications of Gaussian Subordinated Lévy Fields
%U https://doi.org/10.1007/s11009-023-10033-2
%V 25
%X 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.
@article{merkle2023properties,
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.},
added-at = {2023-12-05T15:28:19.000+0100},
author = {Merkle, Robin and Barth, Andrea},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2731ed72b68fbd1927fa4b95f67ad3e3c/mathematik},
doi = {10.1007/s11009-023-10033-2},
interhash = {88a6564de96171e7e9fcadda85f624ac},
intrahash = {731ed72b68fbd1927fa4b95f67ad3e3c},
issn = {1573-7713},
journal = {Methodology and Computing in Applied Probability},
keywords = {},
language = {eng},
pages = 62,
publisher = {Springer},
timestamp = {2023-12-05T15:28:19.000+0100},
title = {On Properties and Applications of Gaussian Subordinated Lévy Fields},
url = {https://doi.org/10.1007/s11009-023-10033-2},
volume = 25,
year = 2023
}
