On filtering for an Ito-Volterra process over vector discontinuous observations

The present paper aims to design the optimal filter for an Ito-Volterra process over vector discontinuous observations. The consideration of a vector measure in an observation equation is to ensure that the uniqueness for a solution to filtering equations is needed to impose the conditions of the Frobenius type on the right-hand sides. There exist two methods for defining a solution to integral equations in vector distribution, however, it is possible to design filtering equations with a measure describing the optimal solution in a common form in both cases