Palm distributions are critical in the study of point processes. In the present paper we focus on a point process $\Phi$ defined as the superposition, i.e., sum, of two independent point processes, say $\Phi = \Phi_1 + \Phi_2$, and we characterize its Palm distribution. In particular, we show that the Palm distribution of $\Phi$ admits a simple mixture representation depending only on the Palm distribution of $\Phi_j$, as $j=1, 2$, and the associated moment measures. Extensions to the superposition of multiple point processes, and higher order Palm distributions, are treated analogously.

翻译：Palm分布在点过程研究中至关重要。本文聚焦于定义为两个独立点过程叠加（即求和）的点过程$\Phi$，即$\Phi = \Phi_1 + \Phi_2$，并刻画其Palm分布。特别地，我们证明了$\Phi$的Palm分布具有一个简单的混合表示，该表示仅依赖于$\Phi_j$（$j=1, 2$）的Palm分布及其关联的矩测度。类似地，我们将结果推广到多个点过程的叠加以及高阶Palm分布的情形。