On central limit theorems for power variations of the solution to the stochastic heat equation

Markus Bibinger; Mathias Trabs

On central limit theorems for power variations of the solution to the stochastic heat equation

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arxiv 1901.01026 v2 pith:75MN2ROZ submitted 2019-01-04 math.ST math.PRstat.TH

Markus Bibinger , Mathias Trabs This is my paper · ORCID

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keywords centralequationheatlimitpowersolutionstochasticvariations

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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
math.PR 2019-08 accept novelty 8.0 of 10

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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