High-frequency analysis of parabolic stochastic PDEs
Statistics Theory
2020-06-02 v4 Probability
Methodology
Statistics Theory
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 a 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
Cite
@article{arxiv.1806.06959,
title = {High-frequency analysis of parabolic stochastic PDEs},
author = {Carsten Chong},
journal= {arXiv preprint arXiv:1806.06959},
year = {2020}
}
Comments
Including supplementary material; accepted for publication in the Annals of Statistics