On Parameters Estimation in Stochastic Differential Equations with Additive Random Effects

Abstract

In this paper, we proposed a class of statistical models where random effects are inserted into a Stochastic differential equations (SDEs) model, SDE defined N independent stochastic processes  the drift term depending on a random variable. The distribution of the random effect depended on unknown parameters which are to be estimated from the continuous observation of the processes. When the drift term is defined linearly and  has Gaussian distribution, we obtained an expression of the exact likelihood and proved the consistency and asymptotic normality of the maximum likelihood estimators.