Parametric inference for stochastic differential equations with random effects in the drift coefficient

In this paper we focus on estimating the parameters in the stochastic differential equations (SDE’s) with drift coefficients depending linearly on a random variables and .The distributions of the random effects and are depends on unknown parameters from the continuous observations of the independent processes . When is an unknown parameter or restrict positive constant also studied in this paper. We propose the Gaussian distribution for the random effect and the exponential distribution for the random effect , we obtained an explicit formulas for the likelihood functions in each case and find the maximum likelihood estimators of the unknown parameters in the random effects and for the unknown parameter . Consistency and asymptotic normality are studied just when is normal random effect and is constant.