On filtering problems over Ito-Volterra and delayed observations

摘要

In this paper, the Kalman-Bucy filter is designed for an Ito-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 optimal filtering equations over observations with delays are obtained for an Ito-Volterra process, proceeding from discontinuous observations of the Ito-Volterra type. It is shown that the designed filter can be significantly simplified for a dynamic system state governed by a differential equation. The filtering problems are considered over observations with multiple delays and a set of delays of the continuum power.