Abstract
The problem of finite dimensional realization in filtering is addressed, both in continuous time and discrete time. It can be treated within the same framework by introducing the symmetry semi group of a deterministic evolution equation. We show how this semi group can support a finite dimensional realization.
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References
J.S. Baras, “Group invariance methods in nonlinear filtering of diffusion processes”, Stochastic Systems: The Mathematics of Filtering and Identification and Applications, M.Hazewinkel and J.C.Willems (eds), Reidel, Dordrecht, The Netherlands (1981), 565–572.
M.H.A. Davis, S.L Marcus, “An introduction to non linear filtering”, Stochastic Systems: The Mathematics of Filtering and Identification and Applications, M.Hazewinkel and J.C.Willems (eds), Reidel, Dordrecht, The Netherlands (1981), 53–75.
G.B. Di Masi and W.J. Runggaldier, “On measure transformations for combined filtering and parameter estimation in discrete time”, Systems and Control Letters, 2 (1982), 57–62.
A. Friedman, “Stochastic Differential Equations and Applications”, I, Academic Press, New York (1975).
J. Lévine, “Finite dimensional realizations of stochastic P.D.E.’s and application to filtering”, to be published in Stochastics.
R.S. Liptser and A.N. Shiryaev, “Statistics of random processes”, I, Springer-Verlag, Berlin(1977).
P.J. Olver, “Applications of Lie Groups to Differential Equations”, Springer-Verlag, New York (1986).
L. V. Ovsjannikov, “Group Analysis of Differential Equations”, Academic Press, New York (1982).
R.S. Palais, “A global formulation of the Lie theory of transformation groups”, Memoirs of the AMS 22, Providence (1957).
S.I. Rosencrans, “Perturbation algebra of an elliptic operator”, Journal of Mathematical Analysis and Applications, 56 (1976), 317–329.
I. Shigekawa, “Transformations of the brownian motion on the riemannian symmetric space”, Z. Wahr. Werw. Geb., 65 (1984), 493–522.
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© 1991 Birkhäuser Boston
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Cohen de Lara, M. (1991). Application of Symmetry Semi Groups to Discrete and Continuous Time Filtering Problems. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_12
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_12
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
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