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In this work, we present the convergence analysis of one-point largedeviations rate functions (LDRFs) of the spatial finite difference method (FDM)for stochastic wave equations with small noise, which is essentially about theasymptotical limit of minimization problems and not a trivial task for thenonlinear cases. In order to overcome the difficulty that objective functionsfor the original equation and the spatial FDM have different effective domains,we propose a new technical route for analyzing the pointwise convergence of theone-point LDRFs of the spatial FDM, based on the $\Gamma$-convergence ofobjective functions. Based on the new technical route, the intractableconvergence analysis of one-point LDRFs boils down to the qualitative analysisof skeleton equations of the original equation and its numericaldiscretizations.

Convergence analysis of one-point large deviations rate functions of numerical discretizations for stochastic wave equations with small noise