  In this article, we introduce a system of stochastic differential equations
(SDEs) consisting of time-dependent covariates and consider both fixed and
random effects set-ups. We also allow the functional part associated with the
drift function to depend upon unknown parameters. In this general set-up of SDE
system we establish consistency and asymptotic normality of the M LE through
verification of the regularity conditions required by existing relevant
theorems. Besides, we consider the Bayesian approach to learning about the
population parameters, and prove consistency and asymptotic normality of the
corresponding posterior distribution. We supplement our theoretical
investigation with simulated and real data analyses, obtaining encouraging
results in each case.
