Wasserstein bounds in the clt of the mle for the drift coefficient of a stochastic partial differential equation

In this paper, we are interested in the rate of convergence for the central limit theorem of the maximum likelihood estimator of the drift coefficient for a stochastic partial differential equation based on continuous time observations of the Fourier coefficients u_i (t), i = 1, …, N of the solution, over some finite interval of time [0, T]. We provide explicit upper bounds for the Wasserstein distance for the rate of convergence when N → ∞ and/or T → ∞. In the case when T is fixed and N → ∞, the upper bounds obtained in our results are more efficient than those of the Kolmogorov distance given by the relevant papers of Mishra and Prakasa Rao, and Kim and Park.