High-frequency analysis of parabolic stochastic PDEs
The Annals of Statistics · 2020 · Volume 48 · Issue 2
Abstract
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial covariance function of the noise.
Keywords
60H15, 62G20, 62M40, high-frequency observations, martingale limit theorems, multipower variations, SPDEs, Stochastic heat equation, variation functionals, Volatility estimation
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