On ellipsoidal filtering for the Volterra process over vector discontinuous observations

The ellipsoidal filtering problem is considered for the Volterra process over vector discontinuous observations. The ellipsoidal filtering equations are obtained for the center and matrix of an ellipsoid that approximates the set of possible values of the process state. These equations are developed in the form of the Volterra equations with a measure, which enables us to compute jumps of the center and matrix of the approximating ellipsoid at discontinuity points of observations