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High-frequency analysis of parabolic stochastic PDEs
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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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High-frequency analysis of parabolic stochastic PDEs with multiplicative noise
A central limit theorem holds for high-frequency power variations of the stochastic heat equation with multiplicative noise and Riesz spatial covariance of order alpha in (0,1), with no asymptotic bias.
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