论文标题
估计在具有随机初始条件的高阶偏微分方程上的解决方案上方分布的估计值
Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions
论文作者
论文摘要
在本文中，我们考虑了线性分散方程类别的高阶部分微分方程。我们调查了这些方程的解决方案，但要受到可协调的$φ$ -Sub-sub-gaussian过程的随机初始条件的影响。主要的结果是解决方案上方分布的界限。我们介绍了验证一般结果假设并以显式形式编写的过程的过程示例。还针对高斯初始条件的情况指定了主要结果。
In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable $φ$-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition.
