Gaussian fluctuation for spatial average of parabolic Anderson model with Neumann/Dirichlet/periodic boundary conditions
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Abstract:
Consider the parabolic Anderson model $\partial _tu=\frac {1}{2}\partial _x^2u+u\, \eta$ on the interval $[0, L]$ with Neumann, Dirichlet or periodic boundary conditions, driven by space-time white noise $\eta$. Using Malliavin-Stein method, we establish the central limit theorem for the fluctuation of the spatial integral $\int _0^Lu(t\,, x)\, \mathrm {d} x$ as $L$ tends to infinity, where the limiting Gaussian distribution is independent of the choice of the boundary conditions and coincides with the Gaussian fluctuation for the spatial average of parabolic Anderson model on the whole space $\mathbb {R}$.References
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Additional Information
- Fei Pu
- Affiliation: Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing, People’s Republic of China
- MR Author ID: 993216
- ORCID: 0000-0003-0038-297X
- Email: pufeibnu@gmail.com
- Received by editor(s): August 27, 2020
- Received by editor(s) in revised form: August 2, 2021
- Published electronically: December 3, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 2481-2509
- MSC (2020): Primary 60H15, 60H07, 60F05
- DOI: https://doi.org/10.1090/tran/8565
- MathSciNet review: 4391725