Drift theory is an intuitive tool for reasoning about random processes: It allows turning expected stepwise changes into expected first-hitting times. While drift theory is used extensively by the community studying randomized search heuristics, it has seen hardly any applications outside of this field, in spite of many research questions that can be formulated as first-hitting times. We state the most useful drift theorems and demonstrate their use for various randomized processes, including the coupon collector process, winning streaks, approximating vertex cover, and a random sorting algorithm. We also consider processes without expected stepwise change and give theorems based on drift theory applicable in such scenarios. We use these theorems for the analysis of the gambler's ruin process, for a coloring algorithm, for an algorithm for 2-SAT, and for a version of the Moran process without bias. A final tool we present is a tight theorem for processes on finite state spaces, which we apply to the Moran process. We aim to enable the reader to apply drift theory in their own research to derive accessible proofs and to teach it as a simple tool for the analysis of random processes.

翻译：漂移理论是一种直观的工具，用于推理随机过程：它允许将期望的逐步变化转化为期望的首达时间。尽管漂移理论在研究随机搜索启发式算法的社区中被广泛使用，但在该领域之外，它几乎没有得到任何应用，尽管许多研究问题都可以表述为首达时间。我们陈述了最有用的漂移定理，并展示了它们在各种随机过程中的应用，包括优惠券收集过程、连胜记录、顶点覆盖近似问题以及一种随机排序算法。我们还考虑了没有期望逐步变化的过程，并给出了基于漂移理论且适用于此类场景的定理。我们将这些定理用于分析赌徒破产过程、一种着色算法、一种解决2-SAT问题的算法以及一种无偏的Moran过程变体。我们提出的最后一个工具是适用于有限状态空间的紧致定理，并将其应用于Moran过程。我们的目标是使读者能够在自己的研究中应用漂移理论，以推导出易于理解的证明，并将其作为分析随机过程的简单工具进行教学。