This work is devoted to the problem of estimation of the localization of Poisson source. The observations are inhomogeneous Poisson processes registered by the $k\geq 3$ detectors on the plane. We study the behavior of the Bayes estimators in the asymptotic of large intensities. It is supposed that the intensity functions of the signals arriving in the detectors have cusp-type singularity. We show the consistency, limit distributions and the convergence of moments of these estimators.

中文翻译：

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平面上的泊松源定位：尖点情​​况

这项工作致力于解决泊松源定位的估计问题。观察结果是由飞机上的 $k\geq 3$ 探测器记录的非齐次泊松过程。我们研究贝叶斯估计量在大强度渐近线中的行为。假设到达探测器的信号强度函数具有尖峰型奇异性。我们展示了这些估计量的一致性、极限分布和矩的收敛性。