Localization errors in solving stochastic partial differential equations in the whole space
Abstract
Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius $R$. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be exponentially small. As an application, a numerical scheme is presented which combines the localization and the space and time discretisation, and thus is fully implementable.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.05535
 Bibcode:
 2015arXiv150805535G
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Probability;
 60H15;
 60H35;
 65M06
 EPrint:
 Some details added