This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. For the direct problem, it is shown to be well-posed with a unique mild solution. For the inverse problem, the uniqueness is proved for a certain class of functions and the instability is characterized. Numerical experiments are presented to illustrate the reconstructions by using a truncation-based regularization method.

翻译：本文关注的是由分数布朗运动驱动的随机源码波方程式的反源法问题。 根据随机源码,直接问题在于研究随机波方程式的解决方案。 反源码问题在于根据最终时间数据的预期和变量确定源码的统计属性。 对于直接问题,则表明它具有独特的温和解决办法。 对于反源码问题,则证明某类功能的独特性和不稳定性。 数字实验用以脱轨法说明重建情况。