  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.
