We present a relatively simple and mostly elementary proof of the Lévy–Khintchine formula for subordinators. The main idea is to study the Poisson process time-changed by the subordinator. This is a compound Poisson process which is easy to investigate using elementary probabilistic techniques. It turns out that its rate equals the value of the Laplace exponent of the leading subordinator at 1, and all other characteristics of the subordinator affect just the distribution of summands. The technical tools used are conditional expectations, probability generating function and convergence of discrete random variables.

中文翻译：

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从属者Lévy–Khintchine公式的简单证明

我们为下属提供了一个相对简单的Lévy–Khintchine公式的基本证明。主要思想是研究下属随时间变化的泊松过程。这是一个复合的泊松过程，使用基本概率技术很容易研究。事实证明，它的比率等于前级从属者的拉普拉斯指数的值等于1，并且该从属者的所有其他特征仅影响被授权人的分布。使用的技术工具是条件期望，概率生成函数和离散随机变量的收敛性。