On Classical and Bayesian Asymptotics in State Space Stochastic Differential Equations

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 (SDE's). We then extend our asymptotic theory to random effects models based on systems of state space SDE's, covering both independent and identical and independent but nonidentical collections of state space SDE's. 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 SDE's.