Second-order continuous-time non-stationary Gaussian autoregression

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven by Gaussian white noise. The emphasis is on the non-ergodic case, when the roots of the corresponding characteristic equation are not both in the left half-plane. Copyright Springer Science+Business Media Dordrecht 2014