Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces
Journal article, 2020

Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided.

Random fields

Approximation

Compact two-point homogeneous spaces

Angular power spectrum

Covariance kernel

Hölder regularity

Author

Galatia Cleanthous

Trinity College Dublin

Athanasios G. Georgiadis

Trinity College Dublin

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Emilio Porcu

Trinity College Dublin

Millennium Nucleus Center for the Discovery of Structures in Complex Data

Stochastic Processes and their Applications

0304-4149 (ISSN)

Vol. In Press

Approximation and simulation of Lévy-driven SPDE

Swedish Research Council (VR), 2015-01-01 -- 2018-12-31.

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1016/j.spa.2020.02.003

More information

Latest update

7/1/2020 1