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.

翻译：本文研究加性Rosenblatt过程驱动的（可能非线性）随机微分方程解的参数识别问题，以及由此在路径空间上诱导律的奇异性。我们提出了一种联合估计器，可基于有界时间区间内的离散时间观测值同时估计漂移参数、扩散强度与赫斯特指数，并在固定时间区间内的高频渐近框架下证明了该估计量的强相合性（以及收敛速度）。作为该强相合性的推论，我们证明了由不同漂移的解生成测度之间的奇异性，进而表明Rosenblatt过程不满足Girsanov型定理。