Estimation of parameters in stochastic differential equations with two random effects

<p>In this paper we investigate consistency and asymptotic normality of the posterior distribution of the parameters in the stochastic differential equations (SDE’s) with diffusion coefficients depending nonlinearly on a random variables and (the random effects).The distributions of the random effects and depends on unknown parameters which are to be estimated from the continuous observations of the independent processes . We propose the Gaussian distribution for the random effect and the exponential distribution for the random effect , we obtained an explicit formula for the likelihood function and find the estimators of the unknown parameters in the random effects.</p>