High-frequency analysis of parabolic stochastic PDEs with multiplicative noise

Abstract

We consider the stochastic heat equation driven by a multiplicative Gaussian noise that is white in time and spatially homogeneous in space. Assuming that the spatial correlation function is given by a Riesz kernel of order $\alpha \in (0,1)$, we prove a central limit theorem for power variations and other related functionals of the solution. To our surprise, there is no asymptotic bias despite the low regularity of the noise coefficient in the multiplicative case. We trace this circumstance back to cancellation effects between error terms arising naturally in second-order limit theorems for power variations.

"Part I" has been removed from the title

References in corpus (5)

• Multipower variation for Brownian semistationary processes
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• High-frequency analysis of parabolic stochastic PDEs
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