 Abstract : We are interested in the rate of convergence of various approximations of the solutions of second order parabolic stochastic PDEs. We study, in particular, the following type of approximations:
1. Wong-Zakai approximations.
2. Splitting-up and fractional step methods;
3. Finite difference schemes and their generalizations;
4. Galerkin approximations, finite elements.
We obtain sharp estimates on the accuracy of these approximations, and prove results on accelerated numerical schemes by implementing Richardson's extrapolation. Finally we present applications in nonlinear filtering. |
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