Abstract: Let α,T> 0. We study the asymptotic properties of a least squares estimator for the parameter α of a fractional bridge defined as dXt = −α Xt T−t dt + dBt, 0 � t < T, where B is a fractional Brownian motion of Hurst parameter H> 1 2. Depending on the value of α, 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. Also, we compare our results to the (known) case where B is replaced by a standard Brownian motion W. It is great pleasure for us to dedicate this paper to our friend David Nualart, in celebration of his 60th birthday and with all our admiration. hal-00560815, version 3- 2 Aug 2013
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