The filtering problem consists in the estimation of an unknown current state of a dynamical system based on noisy observations. The solution of the filtering problem is a probability measure process which is the conditional distribution of the signal given all the information available at time t, that is given the observation path observed in the interval [0,t]. Under certain assumptions the conditional distribution of the signal satisfies a semi-linear stochastic PDE of parabolic type. The study of this SPDE (existence and uniqueness of the solution) and the properties of its solution (smoothness, stability, long-time asymptotics) is a central theme in nonlinear filtering and a major influence to numerical applications.
In recent years there here been advances on the theoretical analysis of the equation (existence of the solution under general conditions on the coefficients, asymptotic stability, uniqueness, the innovation conjecture has been solved) and on the numerical side (particle approximations, spectral methods, grid methods) and the workshop will discuss (some of) these advances.