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SUMMARY:Accelerated numerical schemes for stochastic partial differential 
 equations - Gyongy\, I (University of Edinburgh)
DTSTART:20120910T101000Z
DTEND:20120910T110000Z
UID:TALK39671@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A class of finite difference and finite element approximations
  are considered for (possibly) degenerate parabolic stochastic PDEs. Suffi
 cient conditions are presented which ensure that the approximations admit 
 power series expansions in terms of parameters corresponding to the mesh o
 f the schemes. Hence\, an implementation of Richardson's extrapolation sho
 ws that the accuracy in supremum norms of suitable mixtures of approximati
 ons\, corresponding to different parameters\, can be as high as we wish\, 
 provided appropriate regularity conditions are satisfied. The results are 
 applied in nonlinear filtering problems of partially observed diffusion pr
 ocesses. The talk is based on recent joint results with Nicolai Krylov on 
 accelerated finite difference schemes\, and joint results with Annie Mille
 t on accelerated finite element approximations. \n
LOCATION:Seminar Room 1\, Newton Institute
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