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 $\Gamma$-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.

翻译：在这项工作中,我们提出对使用小噪音的随机波方程式的空间有限差分法单点大偏差率函数(LDRFs)的集中分析,这主要涉及最小化问题的零点极限,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的客观功能有不同有效域的客观功能的困难,我们提议了一个新的技术途径,根据客观功能的美元-Gamma$-一致,分析空间FDM的单点LDRs的点趋同率函数(LDRFs)。根据新的技术途径,对一点LDRFs的难解趋同分析,归结到对原始方程式及其数字分解的骨形方程进行定性分析。