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April 2003 Exact rates of convergeance for a branching particle approximation to the solution of the Zakai equation
Dan Crisan
Ann. Probab. 31(2): 693-718 (April 2003). DOI: 10.1214/aop/1048516533

Abstract

In Crisan, Gaines and Lyons [SIAM J. Appl. Probab. 58 (1998) 313--342] 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.

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Dan Crisan. "Exact rates of convergeance for a branching particle approximation to the solution of the Zakai equation." Ann. Probab. 31 (2) 693 - 718, April 2003. https://doi.org/10.1214/aop/1048516533

Information

Published: April 2003
First available in Project Euclid: 24 March 2003

zbMATH: 1137.60335
MathSciNet: MR1964946
Digital Object Identifier: 10.1214/aop/1048516533

Subjects:
Primary: 60G57 , 65U05 , 93E11

Keywords: branching algorithm , Filtering , Monte Carlo approximation , Particle filters , Zakai equation

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2003
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