Wong, Wing Shing On a new class of finite dimensional estimation algebras. (English) Zbl 0628.93068 Syst. Control Lett. 9, 79-83 (1987). 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 Cited in 1 ReviewCited in 17 Documents 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 Keywords:nonlinear filters; finite dimensional Lie algebras; estimation algebra; partially observed diffusion Citations:Zbl 0458.60030 PDFBibTeX XMLCite \textit{W. S. Wong}, Syst. Control Lett. 9, 79--83 (1987; Zbl 0628.93068) Full Text: DOI References: [1] Wong, W. S., New classes of finite-dimensional nonlinear filters, Systems Control Lett., 3, 155-164 (1983) · Zbl 0529.93060 [2] Bend, V. E., Exact finite-dimensional filters for certain diffusions with nonlinear drift, Stochastics, 5, 65-92 (1981) · Zbl 0458.60030 [3] Bend, V. E., New exact nonlinear filters with large Lie algebras, Systems Control Lett., 5, 217-221 (1985) · Zbl 0562.93076 [4] Zeitouni, O.; Bobrovski, B. Z., Another approach to the equation of nonlinear filtering and smoothing with applications (1984), Preprint [5] Shukhman, T., Explicit filters for linear systems and certain nonlinear systems with stochastic initial conditions (1985), Preprint [6] Haussmann, U. G.; Pardoux, E., A conditionally almost linear filtering problem with non-Gaussian initial condition (1986), Preprint · Zbl 0641.60050 [7] Daum, F. E., Exact solution to the Zakai equation for certain diffusions, (Proc. 24th IEEE. Conf Decision and Control (1985)), 1964-1965 [8] Lancaster, P.; Rodman, L., Existence and uniqueness theorems for the algebraic Riccati equation, Internal. J. Control, 32, 285-309 (1980) · Zbl 0439.49011 [9] Gantmacher, F. R., Theory of Matrices (1959), Chelsea: Chelsea New York · Zbl 0085.01001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.