Des resultats de non existence de filtre de dimension finie

We show that a necessary condition for the existence of a universal finite dimensionally computable filter is that the Lie algebra $ naturally associated with the Zakai' equation, be finite dimensional at each point and that there exists a homomorphism from a Lie algebra of vectors fields onto.Conversely, we show that, if the signal is one dimensional and if S is infinite dimensional at each point of R, then only the constant functions are such the filter ntf can be realized as theimage of a diffusion.