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.
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