标题： 从连续噪声数据中估计Hurst参数 显示英文标题

标题： Estimation of the Hurst parameter from continuous noisy data

摘要： 本文解决了从连续时间噪声样本中估计分数布朗运动的Hurst指数的问题。 在考虑的设置下，只有当观测区间长度趋于无穷大或噪声强度趋于零时，才能进行一致估计。 主要结果是在这两种情况下模型的局部渐近正态性（LAN）的证明，这揭示了最优最小最大率。 显示英文摘要

摘要： This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under consideration is possible only if either the length of the observation interval increases to infinity or intensity of the noise decreases to zero. The main result is a proof of the Local Asymptotic Normality (LAN) of the model in these two regimes, which reveals the optimal minimax rates.