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