Maximum likelihood estimation for stochastic differential equations with random effects

Abstract : We consider $N$ independent stochastic processes $(X_i(t), t\in [0,T_i])$, $i=1,\ldots, N$, defined by a stochastic differential equation with drift term depending on a random variable $\phi_i$. The distribution of the random effect $\phi_i$ depends on unknown parameters which are to be estimated from the continuous observation of the processes $X_i$. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect $\phi_i$ and $\phi_i$ has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when $T_i=T$ for all $i$ and $N$ tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large.
Type de document :
Article dans une revue
Scandinavian Journal of Statistics, Wiley, 2013, 40 (2), pp.322-343. <10.1111/j.1467-9469.2012.00813.x/abstract>
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00650844
Contributeur : Adeline Samson <>
Soumis le : lundi 12 décembre 2011 - 13:26:13
Dernière modification le : mercredi 4 janvier 2017 - 16:21:14
Document(s) archivé(s) le : vendredi 16 novembre 2012 - 15:12:35

Fichier

submission_delattre_etal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Maud Delattre, Valentine Genon-Catalot, Adeline Samson. Maximum likelihood estimation for stochastic differential equations with random effects. Scandinavian Journal of Statistics, Wiley, 2013, 40 (2), pp.322-343. <10.1111/j.1467-9469.2012.00813.x/abstract>. <hal-00650844>

Partager

Métriques

Consultations de
la notice

249

Téléchargements du document

173