Markov modelIn probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.
Complete metric spaceIn mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g. is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below).
Historically informed performanceHistorically informed performance (also referred to as period performance, authentic performance, or HIP) is an approach to the performance of classical music, which aims to be faithful to the approach, manner and style of the musical era in which a work was originally conceived. It is based on two key aspects: the application of the stylistic and technical aspects of performance, known as performance practice; and the use of period instruments which may be reproductions of historical instruments that were in use at the time of the original composition, and which usually have different timbre and temperament from their modern equivalents.
