Eric Hall: Richardson extrapolation and finite difference schemes for SPDEs

Stochastic partial differential equations (SPDEs) are used
in many areas of applied science and engineering. Examples of systems
that are modeled by SPDEs arise in applications as diverse as
satellite guidance, tumor detection and financial markets. In many
instances analytic solutions to these equations are unavailable and
approximations with a high order of accuracy are difficult to obtain.

We will recall an extrapolation technique known as Richardson's
method. We will then consider finite difference approximations for an
important class of SPDEs and give sufficient conditions under which
the strong rate of convergence with respect to the spatial
approximation can be accelerated to an arbitrarily high order by
Richardson's method.