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Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift. (English) Zbl 1189.60058

Summary: Some deviation inequalities and moderate deviation principles for the maximum likelihood estimators of parameters in an Ornstein-Uhlenbeck process with linear drift are established by the logarithmic Sobolev inequality and the exponential martingale method.

MSC:

60F10 Large deviations
62F12 Asymptotic properties of parametric estimators
62M05 Markov processes: estimation; hidden Markov models
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