散粒噪声Cox随机球的宏观分析
Macroscopic analysis of shot-noise Cox random balls
摘要：
本文考虑了由散粒噪声Cox过程生成的加权欧氏随机球的聚类模型。它是簇点过程的一个例子。我们通过缩小球的半径对模型进行缩放，并通过增加每个簇中的球的（平均）数量或/和增加簇的（平均）数量来补偿这种影响。我们考虑两种不同的场景，比如局部场景和全局场景。启发式地，在第一种情况下，我们关注集群中大球的平均数量，而在第二种情况下，我们关注模型中大球的全局平均数量。根据不同的情景，集群结构可以持续到极限或消失。
英文摘要：
In this paper, we consider a cluster model of weighted Euclidean random balls generated by a shot-noise Cox process. It is an example of cluster point process. We perform a scaling on the model by shrinking the radii of the balls and compensate this effect by increasing the (mean) number of balls in each cluster, or/and increasing the (mean) number of clusters. We consider two different scenarios, say a local and a global scenarios. Heuristically, in the first scenario, we focus on the mean number of large balls in a cluster while in the second one, we focus on the global mean number of large balls in the model. According to the different scenarios, the cluster structure can persist at the limit or disappear.
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