Wasserstein Bounds in the CLT of the MLE for the Drift Coefficient of a Stochastic Partial Differential Equation

Abstract

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 ui(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.