Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60G35 Applications (signal detection, filtering, etc.), See Also {62M20, 93E10, 93E11, 94Axx}
- 60F17 Functional limit theorems; invariance principles
- 93E11 Filtering, See also {60G35}

**Résumé:** We give give a review of some Monte-Carlo methods for
numerically solving the non-linear filtering equation associated with a
discrete-time or continuous-time Markov state process and a discrete-time
observation process. These methods are based on interacting particle systems,
which have been introduced earlier, for example in
\cite{DJP98}, \cite{DJ99} or \cite{DM99}. Here we first state again the results
of these previous papers, with only very short hints for the proofs,
and with emphasis on the central limit theorem obtained as the number
of particles (hence the time necessary to perform the procedure) increases. We
also state and prove some new results concerning the case where the setting of
the dynamical system, that is the initial law, the transition probabilities
and/or the mathematical description of the observation noise are unperfectly
known.

**Mots Clés:** *Filtering ; Monte-Carlo methods ; Diffusion processes ; Interacting particle systems*

**Date:** 1999-12-10

**Prépublication numéro:** *PMA-552*