Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central rôle in nonlinear filtering. More precisely, the conditional distribution of a partially observed diffusion solves the normalized version of an equation of this type. We show that
one can approximate the solution of the SPDE by the (unweighted) empirical measure of a finite system of interacting particle for the case when the diffusion evolves in a compact state space with reflecting boundary. This approximation differs from existing approximations where the particles
are weighted and the particle interaction arises through the choice of the weights and not at the level of the particles' motion as it is the case in this work. The system of stochastic differential equations modelling the trajectories of the particles is approximated by the recursive projection
scheme introduced by Pettersson [Stoch. Process. Appl. 59(2) (1995), pp. 295–308].
No Reference information available - sign in for access.
No Citation information available - sign in for access.
No Supplementary Data.
No Article Media
diffusions with reflecting boundary;
interacting particle systems;
stochastic partial differential equations
Document Type: Research Article
Department of Mathematics, Imperial College London, 180 Queen's Gate, London,SW7 2BZ, UK
Department of Mathematics, University of Tennessee, Knoxville, TN,37996-1300, USA
Publication date: May 4, 2014