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

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

Inference for Stochastic Processes

Auteur(s):

Code(s) de Classification MSC:

Résumé: We present a review, without proofs, of some of the methods used for estimating an unknown parameter occuring in the coefficients of a diffusion process, under various observation schemes. These schemes are mostly doscrete in time, along a regular grid, with say $n$ observations, and we are mainly interested in asymptotically good (or even optimal) statistical procedures, in various limiting situations: the mesh of the grid is constant, or it goes to $0$ at some rate in function of the number $n$. We make an attempt to compare the pro and con of those methods. We also consider a situation not so commonly studied so far by statisticians namely the case where each obsevation is made with a measurement error, in two cases: the error is an additive error, or it is a round-off error.

Mots Clés: Diffusion processes ; asymptotic statistical theory ; LAN property ; estimating functions

Date: 2001-09-06

Prépublication numéro: PMA-683