Balan, Raluca, Xia, Panqiu and Zheng, Guangqu
2025.
Almost sure central limit theorem for the hyperbolic Anderson model with Lévy white noise.
Proceedings of the American Mathematical Society
153
, pp. 3083-3098.
10.1090/proc/17204
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Abstract
In this paper, we present an almost sure central limit theorem (ASCLT) for the hyperbolic Anderson model (HAM) with a Lévy white noise in a finite-variance setting, complementing a recent work by Balan and Zheng [Trans. Amer. Math. Soc. 377 (2024), pp. 4171–4221] on the (quantitative) central limit theorems for the solution to the HAM. We provide two different proofs: one uses the Clark-Ocone formula and takes advantage of the martingale structure of the white-in-time noise, while the other is obtained by combining the second-order Gaussian Poincaré inequality with Ibragimov and Lifshits’ method of characteristic functions. Both approaches are different from the one developed in the PhD thesis of C. Zheng [Multi-dimensional Malliavin-Stein method on the Poisson space and its applications to limit theorems (PhD dissertation), Université Pierre et Marie Curie, Paris VI, 2011], allowing us to establish the ASCLT without lengthy computations of star contractions. Moreover, the second approach is expected to be useful for similar studies on SPDEs with colored-in-time noises, when the former approach, based on Itô calculus, is not applicable.
| Item Type: | Article |
|---|---|
| Date Type: | Published Online |
| Status: | In Press |
| Schools: | Schools > Mathematics |
| Publisher: | American Mathematical Society |
| ISSN: | 1088-6826 |
| Date of First Compliant Deposit: | 26 May 2025 |
| Date of Acceptance: | 3 January 2025 |
| Last Modified: | 19 Jun 2025 09:30 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/178507 |
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