Volume 19, 2007Conference Oxford sur les méthodes de Monte Carlo séquentielles
|Page(s)||18 - 21|
|Published online||30 October 2007|
An approximate McKean-Vlasov model for the stochastic filtering problem
Department of Mathematics, Imperial College London, London SW7 2BZ, UK.
2 Department of Mathematics, University of Tennessee, Knoxville TN 37996-1300, USA.
The solution of the stochastic filtering problem is approximated using Clark's robust representation approach [Proc. 2nd NATO Advanced Study Inst., Darlington, 1977, pp. 721–734]. The ensuing approximation is shown to coincide with the time marginals of solutions of a certain McKean-Vlasov type process. The result leads to a representation of the solution of the stochastic filtering problem as a limit of empirical distributions of systems of equally weighted particles. A similar representation has been introduced by Del Moral and Miclo in [Stochastic Process. Appl. 86 (2000), no. 2, 193–216.] in the context of Feynman-Kac formulae. The representation introduced below differs from the one introduced in [Del Moral and Miclo, Stochastic Process. Appl. 86 (2000), no. 2, 193–216.] as it involves processes with no jumps.
© EDP Sciences, ESAIM, 2007
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