Parameter estimation for SPDEs based on discrete observations in time and space

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on discrete grid fixed bounded domain. Considering an infill asymptotic regime both coordinates, we prove central limit theorems realized quadratic variations based temporal and spatial increments as well double time space. Resulting method of moments estimators diffusivity volatility parameter inherit normality can be constructed robustly with respect to sampling frequencies Upper lower bounds reveal that general optimal convergence rate joint parameters slower than usual parametric rate. The theoretical results are illustrated numerical example.