FINITE-DIMENSIONAL FILTERS .2. INVARIANCE GROUP TECHNIQUES

This two-part paper deals with necessary or sufficient conditions for the existence of finite-dimensional filters. In the first part, we set the problem and proposed a construction of finite-dimensional filters by the Wei-Norman technique. In this second part, we shaw how geometr ic-methods offer another approach that is more powerful, as we shall s ee, The invariance group of a parabolic equation is introduced and its action on initial data enhanced. This is applied to the problem of fi nite-dimensional realization of bilinear stochastic PDEs and further s implified by the introduction of a Riemannian framework. We end by an analysis of partially observed systems having finite-dimensional filte rs, with emphasis on the case of systems with correlated noise.