Finite-dimensional approximations for the equation of nonlinear filtering derived in mild form (Q579749)

In this paper, the authors establish a mild form of the Zakai equation for the unnormalized density in the uncorrelated filtering theory setting. Under suitable assumptions on the signal process, a continuity property of the solution with respect to the initial state, the semi- group and the forcing operator is proved. This provides convergence criteria for finite-dimensional Galerkin approximations involving only the linear deterministic part of the Zakai equation.