论文标题
随机热方程的极端和添加剂Lévy噪声
Extremes of the stochastic heat equation with additive Lévy noise
论文作者
论文摘要
我们分析了溶液的空间渐近特性，该方程是由添加剂时空白噪声驱动的随机热方程。在固定的时间$ t> 0 $和空间$ x \ in \ mathbb {r}^d $中，我们确定解决方案的确切尾巴行为，包括轻尾和重尾Lévy跳跃措施。基于这些渐近药，我们确定任何固定时间$ t> 0 $ $ | x |的差异$ t> | \ to \ infty $。
We analyze the spatial asymptotic properties of the solution to the stochastic heat equation driven by an additive Lévy space-time white noise. For fixed time $t > 0$ and space $x \in \mathbb{R}^d$ we determine the exact tail behavior of the solution both for light-tailed and for heavy-tailed Lévy jump measures. Based on these asymptotics we determine for any fixed time $t> 0$ the almost-sure growth rate of the solution as $|x| \to \infty$.
