  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.
