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Identification of the point sources in some stochastic wave equations. (English) Zbl 1470.60183

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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R30 Inverse problems for PDEs
35R60 PDEs with randomness, stochastic partial differential equations
62H12 Estimation in multivariate analysis
62M09 Non-Markovian processes: estimation
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