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

Abstract

We construct a sequence of branching particle systems αn 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 n1/4. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far.