论文标题
随机波方程与时间无关的噪声的精确渐近学
Exact asymptotics of the stochastic wave equation with time-independent noise
论文作者
论文摘要
在本文中，我们研究了所有维度的随机波方程$ d \ leq 3 $，由高斯噪声$ \ dot {w} $驱动，不取决于时间。我们假设噪声是白色的，或者噪声的协方差函数满足与Riesz内核相似的缩放属性。使用malliavin conculus在skorohod的意义上解释了该溶液。我们获得了$ p $ - 解决方案的确切渐近行为。对于关键案例，当$ d = 3 $并且噪声为白色时就是这种情况，我们获得了第二瞬间的确切过渡时间。
In this article, we study the stochastic wave equation in all dimensions $d\leq 3$, driven by a Gaussian noise $\dot{W}$ which does not depend on time. We assume that either the noise is white, or the covariance function of the noise satisfies a scaling property similar to the Riesz kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We obtain the exact asymptotic behaviour of the $p$-th moment of the solution either when the time is large or when $p$ is large. For the critical case, that is the case when $d=3$ and the noise is white, we obtain the exact transition time for the second moment to be finite.
