Sharp Large Deviations for the Ornstein - Uhlenbeck Process
نویسندگان
چکیده
منابع مشابه
Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process
For the Ornstein-Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding of this trichotomy, we investigate sharp large deviation principles for this estimator in the three situations. In the explosive case, we exhibit a very unusual rate function with a shaped flat v...
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We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half. A.M.S. Classification: 60F10, 60G15, 60J65
متن کاملLarge deviations for the Ornstein-Uhlenbeck process with shift
We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical non-steepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation...
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Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...
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Langevin-like equations have been studied in the presence of arbitrary noise. The characteristic functional of the generalized Langevin process has been built up. Exact results for all cumulants are given. Particular stress has been put on the Campbell, dichotomous and radioactive decay noises. Transient relaxation, susceptibility and diffusion constants for different (noisy) media have been sk...
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ژورنال
عنوان ژورنال: Теория вероятностей и ее применения
سال: 2001
ISSN: 0040-361X
DOI: 10.4213/tvp3952