Central limit theorems for approximating ergodic limit of SPDEs via a full discretization

In this talk, we focus on characterizing quantitatively the fluctuations between the ergodic limit and the time-averaging estimator of the full discretization for the parabolic stochastic partial differential equation. We establish a central limit theorem, which shows that the normalized time-averaging estimator converges to a normal distribution with the variance being the same as that of the continuous case, where the scale used for the normalization corresponds to the temporal strong convergence rate of the considered full discretization.