On filtering over Îto–Volterra observations

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.