A feasible central limit theorem for realised covariation of SPDEs in the context of functional data
函数型数据中随机偏微分方程实现协变差的可行中心极限定理
This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup adjusted…