论文标题
对随机波方程的数值离散率的一分偏差率函数的收敛分析，其噪声较小
Convergence analysis of one-point large deviations rate functions of numerical discretizations for stochastic wave equations with small noise
论文作者
论文摘要
在这项工作中，我们介绍了空间有限差异方法（FDM）的单点大偏差速率函数（LDRF）的收敛分析，用于具有较小噪声的随机波方程，这本质上是关于最小化问题的渐近限制，而不是非线性案例的微不足道任务。为了克服原始方程和空间FDM的目标函数具有不同的有效域的困难，我们提出了一条新的技术途径，以根据$γ$ - 目标函数的$γ$ - 连接，以分析空间FDM的单点LDRF的重点收敛。基于新的技术途径，对单点LDRF的顽固性收敛分析归结为对原始方程及其数值离散化的骨架方程的定性分析。
In this work, we present the convergence analysis of one-point large deviations rate functions (LDRFs) of the spatial finite difference method (FDM) for stochastic wave equations with small noise, which is essentially about the asymptotical limit of minimization problems and not a trivial task for the nonlinear cases. In order to overcome the difficulty that objective functions for the original equation and the spatial FDM have different effective domains, we propose a new technical route for analyzing the pointwise convergence of the one-point LDRFs of the spatial FDM, based on the $Γ$-convergence of objective functions. Based on the new technical route, the intractable convergence analysis of one-point LDRFs boils down to the qualitative analysis of skeleton equations of the original equation and its numerical discretizations.
