On Central Limit Theorems for Power Variations of the Solution to the Stochastic Heat Equation

Abstract

We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a central limit theorem. It generalizes the theory from Bibinger and Trabs (Volatility estimation for stochstic PDEs using high-frequency observations, 2017) [2] in several directions.