An averaging method is applied to derive effective approximation to thefollowing singularly perturbed nonlinear stochastic damped wave equation \nuu_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain$D\subset\R^n$\,, $1\leq n\leq 3$\,. Here $\nu>0$ is a small parametercharacterising the singular perturbation, and $\nu^\alpha$\,, $0\leq \alpha\leq1/2$\,, parametrises the strength of the noise. Some scaling transformationsand the martingale representation theorem yield the following effectiveapproximation for small $\nu$, u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of$\ord{\nu^\alpha}$\,.
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机译：应用平均方法来推导以下开环域上奇异摄动非线性随机阻尼波方程\ nuu_ {tt} + u_t = \ D u + f（u）+ \ nu ^ \ alpha \ dot {W}的有效逼近$ D \ subset \ R ^ n $ \，$ 1 \ leq n \ leq 3 $ \ ,.其中$ \ nu> 0 $是表征奇异摄动的小参数，而$ \ nu ^ \ alpha $ \，即$ 0 \ leq \ alpha \ leq1 / 2 $ \，则是对噪声强度的参数化。对于小$ \ nu $，u_t = \ D u + f（u）+ \ nu ^ \ alpha \ dot {W}，一些缩放变换和and表示定理产生以下有效逼近，误差为$ \ ord {\ nu ^ \ alpha} $ \ ，。
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