Elworthy K.D., Jan Y.L., Li X.-M. The Geometry of Filtering

Springer Basel AG, 2010Filtering is the science of nding the law of a process given a partial observation of it. The main objects we study here are di usion processes. These are naturally associated with second-order linear di erential operators which are semi-elliptic and so introduce a possibly degenerate Riemannian structure on the state space. In fact, much of what we discuss is simply about two such operators intertwined by a smooth map, the \projection from the state space to the observations space",
and does not involve any stochastic analysis.