Mon, 01 Dec 2003
14:15
14:15
DH 3rd floor SR
The solutions to a class of non-linear stochastic partial
differential equations
Jie Xiong
(WIAS and University of Tennessee)
Abstract
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.