A particle approximation of the solution of the Kushner–Stratonovitch equation

Abstract.

We construct a sequence of branching particle systems α _n convergent in measure to the solution of the Kushner–Stratonovitch equation. The algorithm based on this result can be used to solve numerically the filtering problem. We prove that the rate of convergence of the algorithm is of order n ^¼. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far.