This paper is devoted to investigating a time-indexed family of inverse-power integral functionals of Poisson processes. A complete characterization is provided for the probability distributions of the entire family, which covers density functions, cumulative distribution functions and moments. For perpetual functionals equivalent conditions for the strong existence and convergence in powers are established, some explicit asymptotic estimates are derived, and the exponential and Kolmogorov distributions are highlighted as special cases, while for finite-time functionals convergence in powers is established in the weak sense. Tables and graphs are presented for illustrative purposes.

中文翻译：

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关于反幂泊松泛函

本文致力于研究泊松过程的反幂积分泛函的时间索引族。为整个族的概率分布提供了完整的表征，包括密度函数、累积分布函数和矩。对于永续泛函建立幂的强存在性和收敛性的等价条件，推导了一些显式渐近估计，并强调了指数和 Kolmogorov 分布作为特例，而对于有限时间泛函建立了弱意义上的幂收敛. 表格和图表用于说明目的。