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This paper is a survey of recent contributions on estimation in stochasticdifferential equations with mixed-effects. These models involve N stochasticdifferential equations with common drift and diffusion functions but randomparameters that allow for differences between processes. The main objective isto estimate the distribution of the random effects and possibly other fixedparameters that are common to the N processes. While many algorithms have beenproposed, the theoretical aspects related to estimation have been littlestudied. This review article focuses only on theoretical inference forstochastic differential equations with mixed-effects. It has so far only beenconsidered 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, eitherparametric or nonparametric, are discussed. Different schemes of observationsare considered according to the approach, associating a large number ofindividuals with, in most cases, high-frequency observations of thetrajectories.

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