On a new class of finite dimensional estimation algebras
It is now well-known that the so-called estimation algebra of a partially observed diffusion is infinite-dimensional except in some particular cases including the linear case; following Benesh' work [\textit{V. E. Benesh}, Stochastics 5, 65-92 (1981; Zbl 0458.60030)], several papers have dealt with the problem of finding new particular cases; the aim is indeed a better understanding of algebraic properties of the filtering problem. The system studied in this paper consists of a signal solution of \(dx(t)=f(x)dt+Gdw(t)\) where G is a non-singular matrix, and of an observed process of the form \(dy(t)=Hx(t)dt+dv(t)\). A sufficient condition for the estimation algebra to be finite-dimensional is given in terms of two matrix-valued functions; this condition contains both linear and Benesh' filters. Some examples are given.
scientific article; zbMATH DE number 4023172