A review on asymptotic inference in stochastic differential equations with mixed-effects

Maud Delattre (1)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]

This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters that allow for differences between processes. The main objective is to estimate the distribution of the random effects and possibly other fixed parameters that are common to the N processes. While many algorithms have been proposed, the theoretical aspects related to estimation have been little studied. This review article focuses only on theoretical inference for stochastic differential equations with mixed-effects. It has so far only been considered in some very specific classes of mixed-effect diffusion models, observed without measurement error, where explicit estimators can be defined. Within this framework, the asymptotic properties of several estimators, either parametric or nonparametric, are discussed. Different schemes of observations are considered according to the approach, associating a large number of individuals with, in most cases, high-frequency observations of the trajectories.

Mots clés: Asymptotic properties; High-frequency observations; Nonparametric inference; Parametric inference; Random effects; Stochastic differential equations

Domaines: Statistiques [math.ST]

Maud Delattre. A review on asymptotic inference in stochastic differential equations with mixed-effects. Japanese Journal of Statistics and Data Science , 2021, ⟨10.1007/s42081-021-00105-3⟩. ⟨hal-02938697⟩