Identification of the point sources in some stochastic wave equations (Q1722375)

Summary: We introduce and study a type of (one-dimensional) wave equations with noisy point sources. We first study the existence and uniqueness problem of the equations. Then, we assume that the locations of point sources are unknown but we can observe the solution at some other location continuously in time. We propose an estimator to identify the point source locations and prove the convergence of our estimator.