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On a new class of finite dimensional estimation algebras. (English) Zbl 0628.93068

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 [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.
Reviewer: J.Picard

MSC:

93E11 Filtering in stochastic control theory
17B99 Lie algebras and Lie superalgebras
93C10 Nonlinear systems in control theory
60J60 Diffusion processes
62M20 Inference from stochastic processes and prediction
93B25 Algebraic methods
93E10 Estimation and detection in stochastic control theory

Citations:

Zbl 0458.60030
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References:

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