Before revision:  We establish a central limit theorem for the Hayashi-Yoshida  estimator under HBT in the case where prices process follows a continuous Ito process : we obtain an asymptotic bias.
After revision:  We establish a central limit theorem for the Hayashi-Yoshida estimator under HBT in the case where the price process and the observation price process follow a continuous Ito process : we obtain an asymptotic bias.