A direct approach to deriving filtering equations for diffusion processes
The author gives a derivation of the so-called filtering equation for partially observable diffusion processes on the basis of the \(L_p\)-theory of SPDEs, without using any facts from filtering theory itself. The method of derivation is new and does not require any knowledge of filtering theory. After an introduction given in Section 1, Section 2 contains the statement of the problem and the main result (Theorem 2.10). In Section 3 the main idea of proving Theorem 2.10 is explained, and Section 4 contains necessary facts from the \(L_p\)-theory of SPDEs. The final Section 5 contains the proof of Theorem 2.10.
partially observable diffusion processes
\(L_p\)-theory of stochastic partial differential equations
scientific article; zbMATH DE number 1562974