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On Properties and Applications of Gaussian Subordinated Lévy Fields

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  • Robin Merkle

    (University of Stuttgart)

  • Andrea Barth

    (University of Stuttgart)

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.

Suggested Citation

  • Robin Merkle & Andrea Barth, 2023. "On Properties and Applications of Gaussian Subordinated Lévy Fields," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-33, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10033-2
    DOI: 10.1007/s11009-023-10033-2
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    References listed on IDEAS

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    1. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    2. Li, Jingshi & Wang, Xiaoshen & Zhang, Kai, 2016. "Multi-level Monte Carlo weak Galerkin method for elliptic equations with stochastic jump coefficients," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 181-194.
    3. Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    4. Kristjana Ýr Jónsdóttir & Anders Rønn-Nielsen & Kim Mouridsen & Eva B. Vedel Jensen, 2013. "Lévy-based Modelling in Brain Imaging," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 511-529, September.
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