Exact finite-dimensional filters via systems realization for a class of discrete-time nonlinear systems (Q1061082)

For the restricted class of stochastic discrete-time nonlinear systems of which the dynamics are purely deterministic necessary and sufficient conditions for the existence of a finite dimensional filter are given. These conditions require the finite-dimensionality of an associated function space and they yield an explicit characterization of the filter for the system. The authors also discuss shortly the notion of immersion of a stochastic discrete-time system into other discrete-time systems, in particular linear discrete-time systems.