Convergence of a Branching Particle Method to the Solution of the Zakai Equation

We construct a sequence of branching particle systems Un convergent in distribution to the solution of the Zakai equation. The algorithm based on this result can be used to solve numerically the filtering problem. The result is an improvement of the one presented in a recent paper [Crisan and T. Lyons, Prob. Theory Related Fields, 109 (1997), pp. 217--244], because it eliminates the extra degree of randomness introduced there.

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