Author:
Merkle Robin,Barth Andrea
Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Statistics and Probability
Reference48 articles.
1. Abdulle A, Barth A, Schwab C (2013) Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs. Multiscale Model Simul 11(4):1033–1070. https://doi.org/10.1137/120894725
2. Adams RA, Fournier JJF (2003) Sobolev Spaces, Pure and Applied Mathematics (Amsterdam), vol 140, 2nd edn. Elsevier/Academic Press, Amsterdam
3. Adler RJ, Taylor JE (2007) Random Fields and Geometry. Springer Monographs in Mathematics, Springer, New York
4. Ainsworth M, Oden JT (1997) A posteriori error estimation in finite element analysis. Comput Methods Appl Mech Engrg 142(1–2):1–88. https://doi.org/10.1016/S0045-7825(96)01107-3
5. Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis, 3rd edn. Springer, Berlin, a hitchhiker’s guide