We show that the solutions to the damped stochastic wave equation converge pathwise to the solution of a stochastic heat equation. This is called the Smoluchowski–Kramers approximation. Cerrai and Freidlin have previously demonstrated that this result holds in the cases where the system is exposed to additive noise in any spatial dimension or when the system is exposed to multiplicative noise and the spatial dimension is one. The current paper proves that the Smoluchowski–Kramers approximation is valid in any spatial dimension when the system is exposed to multiplicative noise.

中文翻译：

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在任何空间维上具有乘性噪声的阻尼随机波方程的Smoluchowski-Kramers近似

我们表明，阻尼随机波动方程的解在路径上收敛到随机热量方程的解。这称为Smoluchowski-Kramers逼近。Cerrai和Freidlin先前已证明，在系统暴露于任何空间维度的加性噪声​​的情况下，或当系统暴露于乘法噪声且空间维度为一的情况下，此结果均成立。当前论文证明，当系统暴露于乘法噪声时，Smoluchowski-Kramers逼近在任何空间维度上都是有效的。