标题： 双曲安德森模型与时空齐次高斯噪声 显示英文标题

标题： Hyperbolic Anderson Model with space-time homogeneous Gaussian noise

摘要： 在本文中，我们研究任意空间维数 $d$ 的随机波动方程，其中包含形式为 $\sigma(u)=u$ 的乘法项，该方程在文献中也被称为双曲 Anderson 模型。 该方程受到一种广义高斯噪声的扰动，该噪声在空间和时间上都是齐次的。 我们在 Skorohod 意义下证明了该方程解的存在性和唯一性，以及其样本路径的 Hölder 连续性，在空间噪声谱测度的条件与时间白噪声情况下的条件相同的情况下，无论噪声的时间协方差函数如何。 显示英文摘要

摘要： In this article, we study the stochastic wave equation in arbitrary spatial dimension $d$, with a multiplicative term of the form $\sigma(u)=u$, also known in the literature as the Hyperbolic Anderson Model. This equation is perturbed by a general Gaussian noise, which is homogeneous in both space and time. We prove the existence and uniqueness of a solution of this equation (in the Skorohod sense) and the H\"older continuity of its sample paths, under the same respective conditions on the spatial spectral measure of the noise as in the case of the white noise in time, regardless of the temporal covariance function of the noise.