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
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.
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.