Particle Filters in a Continuous Time Framework

I report on a new class of algorithms for the numerical solution of the continuous time filtering problem. These algorithms are inspired by recent advances in the area of weak approximations for solutions of stochastic differential equations. The algorithms belonging to this class generate approximations of the conditional distribution of the signal in the form of linear combinations of Dirac measures, hence can be interpreted as particle filters or, more precisely, particle approximations to the solution of the filtering problem. The main characteristics of these algorithms are discussed and a convergence result for the entire class is stated.