High-frequency Analysis of Stochastic PDEs

This lecture covers the high-frequency analysis of stochastic partial differential equations (SPDEs) with multiplicative noise, focusing on the stochastic heat equation. Topics include the uniqueness of the mild solution, the regularity of the solution process, and the estimation of parameters of interest from observations. The lecture also delves into normalized power variations, the central limit theorem, and the asymptotic drift process. Various theorems and results are presented, along with related literature and restrictions on the hypotheses. The lecture concludes with discussions on finite variation processes, constants, and references to key works.