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 language | English |
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Pages (from-to) | 2071-2098 |
Number of pages | 28 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 45 |
Issue number | 4 |
Early online date | 2 Jul 2013 |
DOIs | |
Publication status | Published - 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