论文标题
从连续嘈杂数据中估算Hurst参数
Estimation of the Hurst parameter from continuous noisy data
论文作者
论文摘要
本文解决了从连续时间嘈杂样本中估算布朗运动的赫斯特指数的问题。仅当观察区间的长度增加到无穷大或噪声强度降低到零时，只有在考虑的设置中进行一致的估计。主要结果是在这两个方案中模型的局部渐近正态性（LAN）的证明，这揭示了最佳的最小速率。
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.
