IJPAM: Volume 41, No. 5 (2007)

ASYMPTOTIC ESTIMATION FOR RETARDED
STOCHASTIC SYSTEMS

Abdelwahed Namir$^1$, Abdelkrim Bennar$^2$, Mohammed Laklalech$^3$
$^{1,2,3}$Department of Mathematics and Data Processing
Faculty of Sciences - Ben M'sik
University Hassan II
Mohammedia, P.O. Box 7955, Sidi Othoman, Casablanca, MOROCCO
$^1$e-mail: a.namir@yahoo.fr
$^2$e-mail: bennar1@yahoo.fr
$^3$e-mail: laklalech2004@hotmail.com


Abstract.In this paper, we propose an asymptotic estimation for delay stochastic systems excited by a general white noise. By spectrum decomposition, we propose an asymptotic estimator of finitely many state components for those systems. We show that this estimator is consistent in the sens that is asymptotically unibiaised and stable (the convergence of error process is strongly convergent). The main interest of the proposed estimator is that it takes into account the dynamic of the residual modes. For identity estimator, we give sufficient conditions for its existence. To illustrate this work, an example is given.

Received: July 20, 2007

AMS Subject Classification: 93E20, 93E10

Key Words and Phrases: delay stochastic system, spectrum decomposition, asymptotic estimation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 5