 Spatial integral of the solution to hyperbolic Anderson model with time-independent noiseRaluca M. Balan and Wangjun Yuan Stochastic Processes and their Applications, 2022, vol. 152, issue C, 177-207 Abstract: In this article, we study the asymptotic behavior of the spatial integral of the solution to the hyperbolic Anderson model in dimension d≤2, as the domain of the integral gets large (for fixed time t). This equation is driven by a spatially homogeneous Gaussian noise, whose covariance function is either integrable, or is given by the Riesz kernel. The novelty is that the noise does not depend on time, which means that Itô’s martingale theory for stochastic integration cannot be used. Using a combination of Malliavin calculus with Stein’s method, we show that with proper normalization and centering, the spatial integral of the solution converges to a standard normal distribution, by estimating the speed of this convergence in the total variation distance. We also prove the corresponding functional limit theorem for the spatial integral process. Keywords: Hyperbolic Anderson model; Spatially homogeneous Gaussian noise; Malliavin calculus; Stein’s method for normal approximations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:152:y:2022:i:c:p:177-207 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.06.013 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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