Some remarks on estimation algebras (Q1080830)

It is known in nonlinear filtering theory that the existence of a finite dimensional filter requires very restrictive conditions on the so-called ''estimation algebra'', which is an algebra of operators generated by those operators which appear in Zakai's equation. The present paper gives necessary conditions for the estimation algebra to be finite dimensional, and then considers the particular case where the unknown process is a controlled process with random initial condition but without driving noise.