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.
On central limit theorems for power variations of the solution to the stochastic heat equation
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abstract
We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a central limit theorem. It generalizes the theory from arXiv:1710.03519 in several directions.
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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.