We address the problem of estimating the drift parameter in a system of $N$ interacting particles driven by additive fractional Brownian motion of Hurst index \( H \geq 1/2 \). Considering continuous observation of the interacting particles over a fixed interval \([0, T]\), we examine the asymptotic regime as \( N \to \infty \). Our main tool is a random variable reminiscent of the least squares estimator but unobservable due to its reliance on the Skorohod integral. We demonstrate that this object is consistent and asymptotically normal by establishing a quantitative propagation of chaos for Malliavin derivatives, which holds for any \( H \in (0,1) \). Leveraging a connection between the divergence integral and the Young integral, we construct computable estimators of the drift parameter. These estimators are shown to be consistent and asymptotically Gaussian. Finally, a numerical study highlights the strong performance of the proposed estimators.

翻译：我们研究由赫斯特指数\( H \geq 1/2 \)的加性分数布朗运动驱动的\( N \)个相互作用粒子系统中漂移参数的估计问题。考虑在固定区间\( [0, T] \)上连续观测相互作用粒子，我们考察当\( N \to \infty \)时的渐近性质。我们的主要工具是一个类似于最小二乘估计量的随机变量，但由于其依赖于Skorohod积分而不可直接观测。通过建立适用于任意\( H \in (0,1) \)的Malliavin导数的定量混沌传播结果，我们证明了该估计量具有相合性与渐近正态性。借助散度积分与Young积分之间的关联，我们构建了可计算的漂移参数估计量。这些估计量被证明具有相合性与渐近高斯性。最后，数值研究验证了所提估计量的优异性能。