2026-04-14T03:42:21Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4677842024-11-04T05:41:01Zcom_2072_98col_2072_378192

00925njm 22002777a 4500 dc Balan, Raluca M. author Nualart, David author Quer i Sardanyons, Lluís author Zheng, Guangqu author 2022 In this article, we study the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension d= 1 , 2. Under mild assumptions, we provide Lp-estimates of the iterated Malliavin derivative of the solution in terms of the fundamental solution of the wave solution. To achieve this goal, we rely heavily on the Wiener chaos expansion of the solution. Our first application are quantitative central limit theorems for spatial averages of the solution to the hyperbolic Anderson model, where the rates of convergence are described by the total variation distance. These quantitative results have been elusive so far due to the temporal correlation of the noise blocking us from using the Itô calculus. A novel ingredient to overcome this difficulty is the second-order Gaussian Poincaré inequality coupled with the application of the aforementioned Lp-estimates of the first two Malliavin derivatives. Besides, we provide the corresponding functional central limit theorems. As a second application, we establish the absolute continuity of the law for the hyperbolic Anderson model. The Lp-estimates of Malliavin derivatives are crucial ingredients to verify a local version of Bouleau-Hirsch criterion for absolute continuity. Our approach substantially simplifies the arguments for the one-dimensional case, which has been studied in the recent work by [2]. http://hdl.handle.net/2072/467784 Dalang's condition Hyperbolic Anderson model Malliavin calculus Quantitative central limit theorem Riesz kernel Second-order Poincaré inequality Wiener chaos expansion The hyperbolic Anderson model : moment estimates of the Malliavin derivatives and applications