Abstract
The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations defined on the whole space. Sufficient conditions are given for accelerating the convergence of the scheme with respect to the spatial approximation to higher order accuracy by an application of Richardson's method. This work extends the results of Gyöngy and Krylov [SIAM J. Math. Anal., 42 (2010), pp. 2275--2296] to schemes that discretize in time as well as space.
| Original language | English |
|---|---|
| Pages (from-to) | 3162-3185 |
| Number of pages | 24 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 44 |
| Issue number | 4 |
| Early online date | 11 Sept 2012 |
| DOIs | |
| Publication status | Published - 11 Sept 2012 |
Keywords
- SPDE
- Parabolic
- Finite difference methods
- Richardson's method
- Extrapolation
- Numerical analysis
- Stochastic processes
- A priori error analysis