New results on the Gaussian projection filter with small observation noise

Abstract

In this paper we define a one dimensional Gaussian projection filter (GPF) for a one dimensional diffusion and show that it behaves as nicely as the previously studied two dimensional GPF w.r.t. the true state. We extend part of the results on its nice behaviour to systems with bounded but not necessarily Lipschitz drift, and observe that in this case the resulting efficient filter does not depend on the drift itself.