The notion of drift refers to the phenomenon that the distribution, which is\nunderlying the observed data, changes over time. Albeit many attempts were made\nto deal with drift, formal notions of drift are application-dependent and\nformulated in various degrees of abstraction and mathematical coherence. In\nthis contribution, we provide a probability theoretical framework, that allows\na formalization of drift in continuous time, which subsumes popular notions of\ndrift. In particular, it sheds some light on common practice such as\nchange-point detection or machine learning methodologies in the presence of\ndrift. It gives rise to a new characterization of drift in terms of stochastic\ndependency between data and time. This particularly intuitive formalization\nenables us to design a new, efficient drift detection method. Further, it\ninduces a technology, to decompose observed data into a drifting and a\nnon-drifting part.\n