Theory of Signals/Statistics
On ergodic filters with wrong initial data
Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 727-731.

For a class of non-uniformly ergodic partly observable Markov processes, under observations subject to a Wiener process or i.i.d. noise, it is shown that a wrong initial data is forgotten with a certain rate.

On démontre que pour une classe de processus de Markov non-uniformément ergodiques avec des observations perturbées par un mouvement Brownien, le fait d'avoir des données initiales erronées est asymptotiquement oublié. La vitesse de convergence est explicitée.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.04.015
Kleptsyna, Marina L. 1, 2; Veretennikov, Alexander Yu. 2, 3

1 Université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 09, France
2 Institute of Information Transmission Problems, Moscow, Russia
3 University of Leeds, Leeds LS2 9JT, UK
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Kleptsyna, Marina L.; Veretennikov, Alexander Yu. On ergodic filters with wrong initial data. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 727-731. doi : 10.1016/j.crma.2007.04.015. http://www.numdam.org/articles/10.1016/j.crma.2007.04.015/

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