On the generation of conditional densities in nonlinear filtering for McKean-Vlasov systems

We consider state estimation problems for stochastic dynamical systems whose state equations are given by McKean-Vlasov type stochastic differential equations and hence contain a measure term corresponding to the distribution of the solution of the state process. Nonlinear filtering equations in the form of conditional distributions have already been derived in this framework for the joint estimation of the state and the measure term when the measure term is itself random [1]. In this work, we consider a class of estimation problems of the above type and obtain nonlinear filtering equations for the conditional density corresponding to the joint information.