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

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

The Monte-Carlo method for filtering with discrete-time observations: Central Limit Theorems

Auteur(s):

Code(s) de Classification MSC:

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