Parameter estimation for alpha-fractional bridges

Khalifa Es-Sebaiy (1) , Ivan Nourdin (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 IECL - Institut Élie Cartan de Lorraine

Let alpha,T>0. We study the asymptotic properties of a least squares estimator for the parameter alpha of a fractional bridge defined as dX_t=-alpha*X_t/(T-t)dt+dB_t, with t in [0,T) and where B is a fractional Brownian motion of Hurst index H>1/2. Depending on the value of alpha, we prove that we may have strong consistency or not as t tends to T. When we have consistency, we obtain the rate of this convergence as well. Also, we compare our results to the (known) case where B is replaced by a standard Brownian motion W.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Khalifa Es-Sebaiy, Ivan Nourdin. Parameter estimation for alpha-fractional bridges. Malliavin calculus and stochastic analysis : a festschrift in honor of David Nualart, Springer, 583 p., 2013, Springer Proceedings in Mathematics & Statistics, 978-1-4614-5906-4. ⟨hal-00560815v3⟩