minstepunkt

Minstepunkt is a term used in mathematical modeling and computational theory to denote the smallest input value, time, or step at which a discrete process undergoes a change in state or value. The word blends the idea of a minimum with the notion of a point of transition, often in stepwise or event-driven contexts.

Formally, in a discrete process that evolves in steps n = 0, 1, 2, ..., the minstepunkt with respect to a condition P is the smallest n for which P is true. For example, if P(n) expresses that a count reaches or exceeds a target, then the minstepunkt is the earliest step at which the target is reached. In a step function, this point corresponds to the first jump where the function value changes.

Applications of minstepunkt occur in change-point analysis, event-driven simulations, and timing or latency studies where the objective is to identify the earliest triggering event. It can be used to measure responsiveness, detect threshold crossings, or determine scheduling or control points in automated systems.

Variants of the concept include minstepunkt relative to a threshold, first-passage times in stochastic processes, and earliest-change points in piecewise-defined models. The concept is closely related to, but not identical with, more widely used ideas such as first-passage time, change point, or threshold crossing, and its precise meaning can vary by discipline.

Etymology reflects its informal, cross-disciplinary usage, with minstepunkt appearing in educational or theoretical discussions as a concise way to refer to the earliest transition point in a stepped process. See also step function, first-passage time, and change-point analysis.