Bidimensional random effect estimation in mixed stochastic differential model

In this work, a mixed stochastic differential model is studied with two random effects in the drift. We assume that N trajectories are continuously observed throughout a large time interval 0, T]. Two directions are investigated. First we estimate the random effects from one trajectory and give a bound of the \(L^2\)-risk of the estimators. Secondly, we build a nonparametric estimator of the common bivariate density of the random effects. The mean integrated squared error is studied. The performances of the density estimator are illustrated on simulations.