Geodesic
An approximate McKean-Vlasov model for the stochastic filtering problem
Dan Crisan1 ; Jie Xiong2
1 Department of Mathematics, Imperial College London, London SW7 2BZ, UK.
2 Department of Mathematics, University of Tennessee, Knoxville TN 37996-1300, USA.
ESAIM. Proceedings, Tome 19 (2007), pp. 18-21.

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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.
DOI : 10.1051/proc:071904

Dan Crisan 1 ; Jie Xiong 2

1 Department of Mathematics, Imperial College London, London SW7 2BZ, UK.
2 Department of Mathematics, University of Tennessee, Knoxville TN 37996-1300, USA. 
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Dan Crisan; Jie Xiong. An approximate McKean-Vlasov model for the stochastic filtering problem. ESAIM. Proceedings, Tome 19 (2007), pp. 18-21. doi : 10.1051/proc:071904. http://geodesic.mathdoc.fr/articles/10.1051/proc:071904/

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