Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation. (English) Zbl 1137.60335

Summary: In [D. Crisan, J. Gaines and T. J. Lyons, SIAM J. Appl. Math. 58, No. 5, 1568–1590 (1998; Zbl 0915.93060)] we describe a branching particle algorithm that produces a particle approximation to the solution of the Zakai equation and find an upper bound for the rate of convergence of the mean square error. In this paper, the exact rate of convergence of the mean square error is deduced. Also, several variations of the branching algorithm with better rates of convergence are introduced.


60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60G07 General theory of stochastic processes
60G35 Signal detection and filtering (aspects of stochastic processes)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
93E11 Filtering in stochastic control theory


Zbl 0915.93060
Full Text: DOI


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