Parameter Estimation of SDEs with Linear Response Theory

This lecture by the instructor covers the parameter estimation of Stochastic Differential Equations (SDEs) using Linear Response Theory. It discusses the problem statement, the use of quadratic variation and Girsanov formula for estimation, fitting equilibrium statistics, and the linear response operator. The lecture also explores the challenges, such as model error and admissible forcings, and presents examples like Langevin dynamics. It delves into least-square fitting of two-point statistics, orthogonal polynomial surrogate models, algorithms for parameter estimation, convergence issues, and the estimation of equilibrium density. The lecture concludes with discussions on nonparametric density estimation, reproducing kernel Hilbert space, and the consistency of linear response estimation.