Quantitative normal approximations for the ...
Document type :
Article dans une revue scientifique: Article original
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Title :
Quantitative normal approximations for the stochastic fractional heat equation
Author(s) :
Assaad, Obayda [Auteur]
Nualart, David [Auteur]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Viitasaari, Lauri [Auteur]
Nualart, David [Auteur]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Viitasaari, Lauri [Auteur]
Journal title :
Stochastics and Partial Differential Equations: Analysis and Computations
Pages :
223-254
Publisher :
Springer US
Publication date :
2021-06-07
ISSN :
2194-0401
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space–time white noise and ...
Show more >Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space–time white noise and the white-colored noise with spatial covariance given by the Riesz kernel or a bounded integrable function. We show that the spatial average over a ball of radius R converges, as R tends to infinity, after suitable renormalization, towards a Gaussian limit in the total variation distance. We also provide a functional central limit theorem. As such, we extend recently proved similar results for stochastic heat equation to the case of the fractional Laplacian and to the case of general noise.Show less >
Show more >Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space–time white noise and the white-colored noise with spatial covariance given by the Riesz kernel or a bounded integrable function. We show that the spatial average over a ball of radius R converges, as R tends to infinity, after suitable renormalization, towards a Gaussian limit in the total variation distance. We also provide a functional central limit theorem. As such, we extend recently proved similar results for stochastic heat equation to the case of the fractional Laplacian and to the case of general noise.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
Source :
Submission date :
2025-01-24T14:37:48Z
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