Fourier-Hermite expansions for nonlinear filtering (Q2711149)

Since the celebrated work of Kalman and Bucy, recursive filters described by stochastic differential equations have become predominant in filtering of randomly perturbed dynamic systems. The Kalman-Bucy approach was extended to nonlinear systems. According to this theory, the nonlinear filtering problem boils down to solve the Zakai equation for the (a posteriori) filtering distribution of the state process. The objective of this paper is to develop an approach to nonlinear filtering which allows the separation of time-consuming computations involving the coefficients of the system from those dealing with the observation data only. The approach is based on a Cameron-Martin type expansion for nonnormalized optimal filters. An additional advantage of this approach is that it does not require any assumptions on the law of the state process.