International Journal of Engineering, Science and Mathematics
  • Year: 2016
  • Volume: 5
  • Issue: 1

Asymptotic Properties of MLE in Stochastic Differential Equations with Random Effects inthe drift Coefficient

  • Author:
  • Alkreemawi Walaa Khazal1,2, Alsukaini Mohammed Sari1,2, Wang Xiang Jun1
  • Total Page Count: 9
  • Page Number: 210 to 218

1School of Mathematics and statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P.R. China

2Department of Mathematics, College of Science, Basra University, Basra, Iraq

Online published on 22 August, 2016.

Abstract

In this paper, a class of statistical modelsis proposed, where random effects are inserted into onedimensional stochastic differential equations (SDEs) model; SDE defined N independent stochastic processes (Xi(t), t ɛ [0, Ti), i =1,…N. The drift term dependent on a random variableφi, we have been discussedtheparametric estimation of the density of the random effect φi within two kinds of mixed models. Anadditive and multiplicativerandom effect are successively considered, when φi has exponential distribution. We obtained an expression of the exact likelihood and proved the consistency and asymptotic normality of the maximum likelihood estimators.

Keywords

Asymptotic normality, consistency, maximum likelihood estimator, mixed effects stochastic differential equations