On ergodic filters with wrong initial data

Marina L. Kleptsyna; Alexander Yu. Veretennikov

doi:10.1016/j.crma.2007.04.015

Theory of Signals/Statistics

On ergodic filters with wrong initial data

Presented by: Paul Deheuvels

Marina L. Kleptsyna ^1,²; Alexander Yu. Veretennikov ^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

Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 727-731.

Abstract
Résumé

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: 2006-09-26
Accepted: 2007-03-30
Published online: 2007-05-23

DOI: 10.1016/j.crma.2007.04.015

Author's affiliations:

Marina L. Kleptsyna ^{1, 2}; Alexander Yu. Veretennikov ^{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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     title = {On ergodic filters with wrong initial data},
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     pages = {727--731},
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     number = {11},
     year = {2007},
     doi = {10.1016/j.crma.2007.04.015},
     language = {en},
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Marina L. Kleptsyna; Alexander Yu. Veretennikov. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.04.015/

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