Point processes are often used to model the occurrence times of different phenomena, such as heatwaves or spike trains. Many of those problems require to study the independence between nonhommogeneous point processes in time, and this work develops three families of tests to assess that hypothesis. They can be applied to different types of processes, and all together they cover a wide range of situations appearing in real problems. The first family includes two tests for Poisson processes. The second family is based on the close point distance, and the third one on cross dependence functions. An extensive simulation study of the size and power of the tests is carried out and some practical rules to select the most appropriate test in different cases, are provided. The proposed tests are demonstrated on a real data application about the occurrence of extreme heat events in three Spanish locations.

中文翻译：

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及时测试两个非同质点过程之间的独立性

点过程通常用于模拟不同现象的发生时间，例如热浪或尖峰列车。其中许多问题需要及时研究非齐次点过程之间的独立性，这项工作开发了三类测试来评估该假设。它们可以应用于不同类型的过程，并且它们一起涵盖了实际问题中出现的各种情况。第一个系列包括两个泊松过程检验。第二类是基于近点距离，第三类是基于交叉依赖函数。对测试的规模和功效进行了广泛的模拟研究，并提供了一些实用规则，以在不同情况下选择最合适的测试。