Estimation of parameters in stochastic differential equations with two random effects

Mohammed Alsukaini; Walaa Alkreemawi; Xiang-Jun Wang

doi:10.14419/ijamr.v5i2.5996

Authors

Mohammed Alsukaini huazhong university
Walaa Alkreemawi huazhong university
Xiang-Jun Wang huazhong university

DOI:

https://doi.org/10.14419/ijamr.v5i2.5996

Published:

2016-04-18

Keywords:

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 (SDEâ€™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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