  In this paper, we study parameter identification for solutions to (possibly
non-linear) SDEs driven by additive Rosenblatt process and singularity of the
induced laws on the path space. We propose a joint estimator for the drift
parameter, diffusion intensity, and Hurst index that can be computed from
discrete-time observations with a bounded time horizon and we prove its strong
consistency (as well as the speed of convergence) under in-fill asymptotics
with a fixed time horizon. As a consequence of this strong consistency,
singularity of measures generated by the solutions with different drifts is
shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt
processes.
