The thesis contributes to the numerical analysis on statistical inference for stochastic partial differential equations (SPDEs). We study the... Show moreThe thesis contributes to the numerical analysis on statistical inference for stochastic partial differential equations (SPDEs). We study the maximum likelihood estimation problem of the drift parameter for a large class of linear parabolic SPDEs. As in the existing literature on statistical inference for SPDEs, we take a spectral approach, and assume that one path of the first N Fourier modes is observed continuously in a fixed finite time interval [0, T]. We first provide a review of the asymptotic properties of the maximum likelihood estimator (MLE) of the drift parameter in the large number of Fourier modes regime, N ∞, while the time horizon T > 0 is fixed. The main part of this thesis is dedicated to the numerical study of the asymptotic properties of the MLEs for two examples of linear parabolic SPDEs: the one-dimensional stochastic heat equation and a d-dimensional linear, diagonalizable, parabolic SPDE, where d ℕ. For the one-dimensional stochastic heat equation, we perform the sensitivity analysis to assess the effect of changes in model parameters on the speed of convergence of the MLE. For the second linear parabolic SPDE, our simulations verify the theoretical results in the literature that both the consistency and asymptotic normality of the MLE hold for such equation only when d ≥ 2. Show less
