Matérn hard-core processes are classical examples for point processes obtained by dependent thinning of (marked) Poisson point processes. We present a generalization of the Matérn models which encompasses recent extensions of the original Matérn hard-core processes. It generalizes the underlying point process, the thinning rule, and the marks attached to the original process. Based on our model, we introduce processes with a clear interpretation in the context of max-stable processes. In particular, we prove that one of these processes lies in the max-domain of attraction of a mixed moving maxima process.

中文翻译：

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Matérn 硬核过程的推广及其对最大稳定过程的应用

Matérn 硬核过程是通过（标记）泊松点过程的相关细化获得的点过程的经典示例。我们提出了 Matérn 模型的概括，其中包括原始 Matérn 核心流程的最新扩展。它概括了基础点过程、细化规则和附加到原始过程的标记。基于我们的模型，我们在最大稳定过程的背景下引入了具有清晰解释的过程。特别是，我们证明了这些过程之一位于混合移动极大值过程的最大吸引力域中。