High-frequency analysis of parabolic stochastic PDEs with multiplicative noise

Fuente: arXiv
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1. Verfasser: Chong, Carsten
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Veröffentlicht: 2019
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author Chong, Carsten
author_facet Chong, Carsten
contents 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 $α\in (0,1)$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_1908_04145
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle High-frequency analysis of parabolic stochastic PDEs with multiplicative noise
Chong, Carsten
Probability
Statistics Theory
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 $α\in (0,1)$, 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.
title High-frequency analysis of parabolic stochastic PDEs with multiplicative noise
topic Probability
Statistics Theory
url https://arxiv.org/abs/1908.04145