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arXiv · 1806.06959

High-frequency analysis of parabolic stochastic PDEs

Carsten Chong
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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.

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Carsten Chong. 2018-06-18. High-frequency analysis of parabolic stochastic PDEs. https://doi.org/10.1214/19-aos1841

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