Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Isotropic Gaussian random fields on the sphere

by A. Lang

(Report number 2013-26)

Abstract
Sample regularity and fast simulation of isotropic Gaussian random fields on the sphere are for example of interest for the numerical analysis of stochastic partial differential equations and for the simulation of ice crystals or Saharan dust particles as lognormal random fields. We recall the results from SAM Report 2013-15, which include the approximation of isotropic Gaussian random fields with convergence rates as well as the regularity of the samples in relation to the smoothness of the covariance expressed in terms of the decay of the angular power spectrum. As example we construct isotropic Q-Wiener processes out of isotropic Gaussian random fields and discretize the stochastic heat equation with spectral methods.

Keywords: Gaussian random fields, isotropic random fields, Karhunen-Loève expansion, spherical harmonic functions, Kolmogorov-Chentsov theorem, sample Hölder continuity, sample differentiability, stochastic heat equation, spectral Galerkin methods, strong convergence rates

@Techreport{L13_523,
  author = {A. Lang},
  title = {Isotropic Gaussian random fields on the sphere},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-26},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-26.pdf },
  year = {2013}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).