This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent, for example, spatial paths or functions of time. To be able to consider, for example, multivariate FMPPs, we also attach an additional, Euclidean, mark to each point. We indicate how the FMPP framework quite naturally connects the point process framework with both the functional data analysis framework and the geostatistical framework. We further show that various existing stochastic models fit well into the FMPP framework. To be able to carry out nonparametric statistical analyses for FMPPs, we study characteristics such as product densities and Palm distributions, which are the building blocks for many summary statistics. We proceed to defining a new family of summary statistics, so-called weighted marked reduced moment measures, together with their nonparametric estimators, in order to study features of the functional marks. We further show how other summary statistics may be obtained as special cases of these summary statistics. We finally apply these tools to analyse population structures, such as demographic evolution and sex ratio over time, in Spanish provinces.

本文讨论功能标记点过程（FMPP），它们被定义为标记点过程，其中标记是某些（波兰语）功能空间中的随机元素。这样的标记可以表示例如空间路径或时间的函数。为了能够考虑多变量FMPP，我们还在每个点上附加了一个欧几里得标记。我们指出了FMPP框架如何自然地将点流程框架与功能数据分析框架和地统计框架连接起来。我们进一步表明，各种现有的随机模型非常适合FMPP框架。为了能够对FMPP进行非参数统计分析，我们研究了诸如产品密度和Palm分布之类的特征，这些特征是许多摘要统计的基础。为了研究功能标记的特征，我们继续定义一个新的摘要统计系列，即所谓的加权标记的减少矩量度，以及它们的非参数估计量。我们进一步展示如何获得其他摘要统计信息作为这些摘要统计信息的特殊情况。最后，我们使用这些工具来分析西班牙各省的人口结构，例如人口结构演变和一段时间内的性别比。