We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen to be, up to negligeable remainders, independent. We use Stein-Malliavin calculus to prove that this wavelet variation satisfies a multidimensional Central Limit Theorem, with an explicit bound for the Wasserstein distance.

翻译：我们定义了一种基于小波、渐近正态且强相合的估计量，用于估计任意Hermite过程的Hurst参数。该估计量通过考虑如下修正小波变异得到：其中小波系数被巧妙选取，使得它们（除可忽略的余项外）相互独立。我们利用Stein-Malliavin计算证明，该小波变异满足多维中心极限定理，并给出了Wasserstein距离的显式上界。