Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 347-364

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

Copyright © 2000 Michael V. Basin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.