Filtering systems of coupled stochastic differential equations partially observed at high frequency

We consider online analysis of systems of stochastic differential equations (SDEs), from high-frequency data. The class of SDEs we focus on have constant volatility and a drift function that is of gradient form. For these models we present a particle filter that is able to analyse the full data, but whose computational cost does not increase as the frequency of the data increases. The method is based on novel extensions of the exact algorithm for simulation and inference of diffusions, and the filters do not need to introduce any approximations through time-discretisation of the process. The new methods have important practical and theoretical advantages over existing filtering methods for this problem. We demonstrate our method on a number of simulated examples, including two motivated by molecular dynamics