  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.
