Rare-Event Simulation for the Stochastic Korteweg-de Vries Equation
Rare-Event Simulation for the Stochastic Korteweg-de Vries Equation
复制标题
随机 Korteweg-de Vries 方程的罕见事件模拟
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Jingcheng Liu
中科院分区：
文献类型：
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作者：
Gongjun Xu;G. Lin;Jingcheng Liu
本文研究了在随机含时力作用下孤子波U（x，t）动力学的尾概率的渐近分析。孤子波U（x，t）$的动力学过程由具有齐次Dirichlet边界条件的Korteweg-de弗里斯（KdV）方程描述，其中的随机时变力被建模为具有振幅的时变高斯噪声。所考虑的尾概率为$w（B）：=P（sup_{tin[0，T]}U（x，t）>B）$，作为$B 对于某一常数T>0和固定x，可将其解释为流体浅表面上水波或密度分层海洋中长内波振幅的尾概率。我们的目标是刻画$w（B）$的渐近行为，并计算在随机力项下孤子波超过某个阈值事件的尾概率。这种罕见事件的计算$w（B）$是特别有用的快速估计的潜在损害的风险，所涉及的。
An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave $U(x,t)$ under a stochastic time-dependent force is developed. The dynamics of the soliton wave $U(x,t)$ is described by the Korteweg--de Vries (KdV) equation with homogeneous Dirichlet boundary conditions under a stochastic time-dependent force, which is modeled as a time-dependent Gaussian noise with amplitude $epsilon$. The tail probability considered is $w(b):=P(sup_{tin[0,T]}U(x,t)>b)$, as $b oinfty$, for some constant $T>0$ and a fixed $x$, which can be interpreted as tail probability of the amplitude of a water wave on the shallow surface of a fluid or long internal wave in a density-stratified ocean. Our goal is to characterize the asymptotic behaviors of $w(b)$ and evaluate the tail probability of the event that the soliton wave exceeds a certain threshold value under a random force term. Such rare-event calculation of $w(b)$ is especially useful for fast estimation of the risk of the potential damage that co...