This paper is concerned with the time-domain stochastic acoustic scattering problem driven by a spatially white additive Gaussian noise. The main contributions of the work are twofold. First, we prove the existence and uniqueness of the pathwise solution to the scattering problem by applying an abstract Laplace transform inversion theorem. The analysis employs the black box scattering theory to investigate the meromorphic continuation of the Helmholtz resolvent defined on rough fields. Second, based on the piecewise constant approximation of the white noise, we construct an approximate wave solution and establish the error estimate. As a consequence, we develop a PML method and establish the convergence analysis with explicit dependence on the PML layer's thickness and medium properties, as well as the piecewise constant approximation of the white noise.

翻译：本文研究由空间白加性高斯噪声驱动的时域随机声波散射问题。本工作的主要贡献体现在两个方面。首先，通过应用抽象的拉普拉斯变换反演定理，我们证明了散射问题路径解的存在唯一性。该分析采用黑箱散射理论研究定义于粗糙场上的亥姆霍兹预解式的亚纯延拓。其次，基于白噪声的分段常数逼近，我们构造了近似波解并建立了误差估计。由此，我们发展了一种PML方法，并建立了收敛性分析，其中明确给出了收敛结果对PML层厚度、介质属性以及白噪声分段常数逼近的依赖关系。