Model fitting for continuous-time stationary processes from discrete-time data

Let X = {X(t), -[infinity]<t<[infinity]} be a continuous-time stationary process with spectral density [phi]X([lambda]; [theta]), where [theta] is a vector of unknown parameters. Let {[tau]k} be a stationary point process on the real line which is independent of X. The identifiability and the estimation of [theta] from the discrete-time observation {X([tau]k), [tau]k} are considered. The consistency of appropriate estimates as the time Tå[infinity] is extablished and a central limit theorem for is given.