On finite difference schemes for degenerate stochastic parabolic partial differential equations

Finite difference approximations in the space variable for possibly degenerate stochastic parabolic partial differential equations are investigated. Sharp estimates for the rate of convergence are obtained, and sufficient conditions are presented under which the speed of approximations can be accelerated to any given order of convergence by Richardson’s method. The main theorems generalize some results of the author with N. V. Krylov.