Sharp large deviations for the fractional Ornstein-Uhlenbeck process

Bernard Bercu (1, 2, 3) , Laure Coutin (4) , Nicolas Savy (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 ALEA - Advanced Learning Evolutionary Algorithms
3 CQFD - Quality control and dynamic reliability
4 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Probabilités [math.PR]

Bernard Bercu, Laure Coutin, Nicolas Savy. Sharp large deviations for the fractional Ornstein-Uhlenbeck process. SIAM Theory of Probability and its Applications, 2011, 55 (4), pp.575-610. ⟨hal-00386239⟩