Estimation of parameters in stochastic differential equations with two random effects

Abstract

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 ( ( ), ∈ [0, ], = 1, … , ). 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.