  In this article we investigate consistency and asymptotic normality of the
maximum likelihood and the posterior distribution of the parameters in the
context of state space stochastic differential equations (SDEs). We then extend
our asymptotic theory to random effects models based on systems of state space
SDEs, covering both independent and identical and independent but non-identical
collections of state space SDEs. We also address asymptotic inference in the
case of multidimensional linear random effects, and in situations where the
data are available in discretized forms. It is important to note that
asymptotic inference, either in the classical or in the Bayesian paradigm, has
not been hitherto investigated in state space SDEs.
