The solutions to a class of non-linear stochastic partial
differential equations

In this talk, we consider a class of non-linear stochastic partial

differential equations. We represent its solutions as the weighted

empirical measures of interacting particle systems. As a consequence,

a simulation scheme for this class of SPDEs is proposed. There are two

sources of error in the scheme, one due to finite sampling of the

infinite collection of particles and the other due to the Euler scheme

used in the simulation of the individual particle motions. The error

bound, taking into account both sources of error, is derived. A

functional limit theorem is also derived. The results are applied to

nonlinear filtering problems.

This talk is based on joint research with Kurtz.