An example of large deviations for a stationary process

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...

Sample path large deviations of a Gaussian process with stationary increments and regularily varying variance

Sample Path Large Deviations for Squares of Stationary Gaussian Processes

In this paper, we show large deviations for random step functions of type

On large deviations of empirical measures for stationary Gaussian processes

We show that the Large Deviation Principle with respect to the weak topology holds for the empirical measure of any stationary continuous time Gaussian process with continuous vanishing at in nity spectral density. We also point out that Large Deviation Principle might fail in both continuous and discrete time if the spectral density is discontinuous.

Moderate Deviations for Dynamic Model Governed by Stationary Process

We give an example of the moderate deviations for the family (X n t) t≥0 , n ≥ 1 with ˙ X n t = a(X n t) + b(X n t) n √ n k+1 ηtn, where ηt is a stationary process obeying the Wold – decomposition: ηt = R t −∞ h(t − s)dN s with respect to a process Nt with homogeneous independent square integrable increments and 1/2 < k < 1.