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Interacting particle systems approximations of the Kushner-Stratonovitch equation

Part of: Stochastic systems and control Sequential methods Stochastic processes

Published online by Cambridge University Press:  01 July 2016

D. Crişan ,
P. Del Moral  and
T. J. Lyons
D. Crişan*
Affiliation:
University of Cambridge
P. Del Moral*
Affiliation:
Université Paul Sabatier
T. J. Lyons*
Affiliation:
Imperial College
*
∗ Postal address: DPMMS, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
∗∗ Postal address: Lab Stat et Probabilités, CNRS UMR C55830, Bat. 1R1, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France. Email address: delmoral@cict.fr
∗∗∗ Postal address: Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK.
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Abstract

In this paper we consider the continuous-time filtering problem and we estimate the order of convergence of an interacting particle system scheme presented by the authors in previous works. We will discuss how the discrete time approximating model of the Kushner-Stratonovitch equation and the genetic type interacting particle system approximation combine. We present quenched error bounds as well as mean order convergence results.

Keywords

Non-linear filteringfilter approximationerror boundsinteracting particle systemsgenetic algorithms

MSC classification

Primary: 60G35: Signal detection and filtering 93E11: Filtering 62L20: Stochastic approximation
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 3 , September 1999 , pp. 819 - 838
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Work partly supported by CEC Contract no. ERB-FMRX-CT96-0075.

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