Finite Difference Schemes for Stochastic Partial Differential Equations in Sobolev Spaces

Máté Gerencsér*, István Gyöngy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We discuss Lp-estimates for finite difference schemes approximating parabolic, possibly degenerate, SPDEs, with initial conditions from Wmp and free terms taking values in Wmp. Consequences of these estimates include an asymptotic expansion of the error, allowing the acceleration of the approximation by Richardson’s method.

Original languageEnglish
Pages (from-to)77-100
Number of pages24
JournalApplied Mathematics and Optimization
Volume72
Issue number1
Early online date8 Oct 2014
DOIs
Publication statusPublished - Aug 2015

Keywords

  • Cauchy problem
  • Extrapolation to the limit
  • Finite differences
  • Richardson’s method
  • Stochastic PDEs

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