The spatially dependent wave speed of a stochastic wave equation driven by space-time white noise is estimated using the local observation scheme. Given a fixed time horizon, we prove asymptotic normality for an augmented maximum likelihood estimator as the resolution level of the observations tends to zero. We show that the expectation and variance of the observed Fisher information are intrinsically related to the kinetic energy within an associated deterministic wave equation and prove an asymptotic equipartition of energy principle using the notion of asymptotic Riemann-Lebesgue operators.

翻译：利用局部观测方案，对由时空白噪声驱动的随机波动方程的空间相关波速进行估计。在固定时间水平下，我们证明了随着观测分辨率趋于零，增广最大似然估计量的渐近正态性。研究表明，观测Fisher信息的期望与方差本质上关联于相应确定性波动方程中的动能，并借助渐近Riemann-Lebesgue算子概念，证明了能量的渐近均分原理。