Higher Order Spatial Approximations for Degenerate Parabolic Stochastic Partial Differential Equations

Eric Joseph Hall (Lead / Corresponding author)

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation where the parabolicity condition is allowed to degenerate. Such equations arise in the nonlinear filtering theory of partially observable diffusion processes. We show that the convergence of the spatial approximation can be accelerated to an arbitrarily high order, under suitable regularity assumptions, by applying an extrapolation technique.


Original languageEnglish
Pages (from-to)2071-2098
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number4
Early online date2 Jul 2013
DOIs
Publication statusPublished - 2 Jul 2013

Keywords

  • Extrapolation
  • SPDE
  • Spatial approximations
  • Finite difference methods
  • Degenerate parabolic equations
  • Richardson's method
  • Numerical analysis
  • Stochastic processes
  • A priori error analysis

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