Long time asymptotics for some dynamical noise free non-linear filtering problems, new cases

Frédéric Cérou 1
1 MEFISTO
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We are interested here in the long time behaviour of the conditional law for a special case of filtering problem: there is no noise on the state equation and the prior law of the state process concentrate fast in some neighborhood of a limit cycle with strictly negative characteristic exponents. Then assuming a deterministic observability property on the cycle we show the concentration of the conditional law on an arbitrary neighborhood of the current (unknown) state as the time goes to infinity. This work can be considered as illustrating how the tools of dynamical systems theory can be use to study the long time behavior of the filtering process.
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Rapport
[Research Report] RR-2541, INRIA. 1995
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https://hal.inria.fr/inria-00074137
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Soumis le : mercredi 24 mai 2006 - 14:36:10
Dernière modification le : samedi 27 janvier 2018 - 01:31:28
Document(s) archivé(s) le : dimanche 4 avril 2010 - 22:12:41

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Frédéric Cérou. Long time asymptotics for some dynamical noise free non-linear filtering problems, new cases. [Research Report] RR-2541, INRIA. 1995. 〈inria-00074137〉

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