Title: Parameter estimation for fractional stochastic heat equations : Berry-Esséen bounds in CLTs Show Chinese title

Title: 分数随机热方程的参数估计：CLTs中的Berry-Esséen界

Abstract: The aim of this work is to estimate the drift coefficient of a fractional heat equation driven by an additive space-time noise using the Maximum likelihood estimator (MLE). In the first part of the paper, the first $N$ Fourier modes of the solution are observed continuously over a finite time interval $[0, T ]$. The explicit upper bounds for the Wasserstein distance for the central limit theorem of the MLE is provided when $N \rightarrow \infty$ and/or $T \rightarrow \infty$. While in the second part of the paper, the $N$ Fourier modes are observed at uniform time grid : $t_i = i \frac{T}{M}$, $i=0,..,M,$ where $M$ is the number of time grid points. The consistency and asymptotic normality are studied when $T,M,N \rightarrow + \infty$ in addition to the rate of convergence in law in the CLT. Show Chinese abstract

Abstract: 本工作的目的是使用最大似然估计量（MLE）估计由加性时空噪声驱动的分数热方程的漂移系数。 在论文的第一部分，解的前$N$个傅里叶模在有限时间区间$[0, T ]$内被连续观测。 当$N \rightarrow \infty$和/或$T \rightarrow \infty$时，提供了MLE中心极限定理的Wasserstein距离的显式上界。 在论文的第二部分，观察到均匀时间网格上的$N$傅里叶模式：$t_i = i \frac{T}{M}$，$i=0,..,M,$其中$M$是时间网格点的数量。当$T,M,N \rightarrow + \infty$时研究了一致性和渐近正态性，以及CLT中的收敛速度。