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}
- 93E11 Filtering, See also {60G35}

**Résumé:** We study an interacting particle system which allows to
explicitely compute the filtering measure, via Monte-Carlo techniques, for a
discrete-time or continuous-time Markov state process and a discrete-time
observation process. This particle system was introduced and proved to
converge, as the number of particles goes to infinity, in \cite{DJP:1}. Here we
are interested in a precise description of the error, in the sense of a central
limit theorem for the normalized errors. A particular feature is that we take
care of the fact that the transition probabilities for the state process are
usually not explicitely known. We describe the normalizing factor as a
function of the number of particles, and also as a function of the number of
variables which are necessary to simulate (hence of the time actually
necessary to perform the procedure).

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

**Date:** 1999-07-02

**Prépublication numéro:** *PMA-515*