On properties and applications of Gaussian subordinated L\'evy fields

TL;DR

This paper studies Gaussian subordinated Lévy fields, exploring their properties, distributions, and applications in random elliptic PDEs, supported by numerical examples demonstrating their practical utility.

Contribution

It introduces and analyzes Gaussian subordinated Lévy fields, highlighting their distributional properties and application in modeling random diffusion coefficients in PDEs.

Findings

Distributional properties of GSLFs derived

Approximation methods for GSLFs discussed

Numerical examples illustrate theoretical results

Abstract

We consider Gaussian subordinated L\'evy fields (GSLFs) that arise by subordinating L\'evy processes with positive transformations of Gaussian random fields on some spatial domain $\mathcal{D}\subset \mathbb{R}^d$, $d\geq 1$. 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.