Des resultats de non existence de filtre de dimension finie
- 1 January 1984
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 13 (1-2) , 83-102
- https://doi.org/10.1080/17442508408833312
Abstract
We show that a necessary condition for the existence of a universal finite dimensionally computable filter is that the Lie algebra $ naturally associated with the Zakai' equation, be finite dimensional at each point and that there exists a homomorphism from a Lie algebra of vectors fields onto.Conversely, we show that, if the signal is one dimensional and if S is infinite dimensional at each point of R, then only the constant functions are such the filter ntf can be realized as theimage of a diffusion.Keywords
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