Least squares estimator for α-sub-fractional bridges

Let alpha, T > 0. We investigate the asymptotic properties of a least squares estimator (LSE) for the parameter of alpha sub-fractional bridge defined as dX(t) = -alpha X-t/T-t dt + d S-t(H), O <= t < T, X-o = O, where S-H is a sub-fractional Brownian motion of Hurst parameter H is an element of(1/2, 1). Depending on the value of alpha, we prove that we may have strong consistency or not as t -> T. When we have consistency, we obtain the rate of this convergence as well.