Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combinations (i.e., on the observation window in the space domain), minimum contrast estimators are introduced. Strong consistency and asymptotic normality are proved. The results are applied to stochastic wave equation perturbed by Brownian noise and they are illustrated by a numerical simulation.

中文翻译：

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基于观测窗的随机波动方程参数估计

研究了带有两个未知参数的线性随机双曲方程的统计推论。基于对解的坐标或其线性组合的观察（即，在空间域的观察窗口上），引入了最小对比度估计量。证明了强一致性和渐近正态性。将该结果应用于受布朗噪声干扰的随机波动方程，并通过数值模拟对其进行了说明。