On Sequential Monte Carlo Sampling of Discretely Observed Stochastic Differential Equations

This article considers the application of sequential importance resampling to optimal continuous-discrete filtering problems, where the dynamic model is a stochastic differential equation and the measurements are obtained at discrete instances of time. In this article it is shown how the Girsanov theorem from mathematical probability theory can be used for numerically evaluating the likelihood ratios needed by the sequential importance resampling. Rao-Blackwellization of continuous-discrete filtering models is also considered. The practical applicability of the proposed methods is demonstrated with a numerical simulation.