Journal of Applied Mathematics and Stochastic Analysis 
Volume 13 (2000), Issue 4, Pages 347-364
doi:10.1155/S1048953300000319

On filtering over Îto-Volterra observations

Michael V. Basin

Autonomous University of Nuevo Leon, Department of Physical and Mathematical Sciences, Apdo Postal 144-F, San Nicolas de los Garza, Nuevo Leon CP 66450, Mexico

Received 1 September 1998; Revised 1 January 2000

Abstract

In this paper, the Kalman-Bucy filter is designed for an Îto-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solved. Proofs of the theorems substantiating the filtering algorithms are given.