Theory of Stochastic Drift

Abstract. In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. Commonly, the processes under investigation show a bias towards this goal, the stochastic drift. Turning an iteration-wise expected bias into a first time of obtaining a value is the main result of drift theorems. This thesis gives an introduction into the theory of stochastic drift, providing examples and reviewing the main drift theorems available. Furthermore, the thesis explains how these methods can be applied in a variety of contexts, including those where drift theorems seem a counter intuitive choice. Later sections examine related methods and approaches.

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