Estimation of parameters in stochastic differential equations with two random effects
DOI:
https://doi.org/10.14419/ijamr.v5i2.5996Keywords:
Stochastic Differential Equations, Maximum Likelihood Estimator, Nonlinear Random Effects, Posterior Consistency, Posterior Normality.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 . 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.
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Received date: March 12, 2016
Accepted date: April 11, 2016
Published date: April 18, 2016