There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper.

翻译：线性网络上的点过程模型尚显匮乏。针对任意线性网络，我们提出通过变换各向同性高斯过程（该过程用于驱动Cox过程的随机强度函数）的不同方式，构建具有各向同性配对相关函数的Cox过程新模型。具体而言，我们引入线性网络上对数高斯、中断及永久型Cox过程三个模型类别，并首次探讨此类参数族模型的统计推断方法与实际应用。此外，我们设计了线性网络上高斯过程的新型模拟算法，并讨论在本研究所涉Cox过程中应选用测地距离度量还是电阻距离度量。