FISHER INFORMATIONS FROM CONTINUOUS AND DISCRETE OBSERVATIONS OF THE DRIFT OF THE ORNSTEIN-UHLENBECK PROCESS

Abstract

When we consider maximum likelihood estimators for the drift coefficient of the Ornstein-Uhlenbeck process from both the continuous observations and the discrete ones, their asymptotic variances are related to each of Fisher informations. However, it is important to see that discrete observations are more applicable than continuous observations from the practical points of view. After delicate calculations, we show that the Fisher information from discrete observations is, of course, less than the one from continuous observations but almost equal to it, if the discretizing timeinterval is sufficiently small.