Editing Markov chain (section)

===Markovian representations===
In some cases, apparently non-Markovian processes may still have Markovian representations, constructed by expanding the concept of the "current" and "future" states. For example, let ''X'' be a non-Markovian process. Then define a process ''Y'', such that each state of ''Y'' represents a time-interval of states of ''X''. Mathematically, this takes the form:
:<math>Y(t) = \big\{ X(s): s \in [a(t), b(t)] \, \big\}.</math>
If ''Y'' has the Markov property, then it is a Markovian representation of ''X''.

An example of a non-Markovian process with a Markovian representation is an [[autoregressive model|autoregressive]] [[time series]] of order greater than one.<ref>{{cite journal |last1=Doblinger |first1=G. |title=Smoothing of noisy AR signals using an adaptive Kalman filter |journal=9th European Signal Processing Conference (EUSIPCO 1998) |date=September 1998 |pages=781–784 |url=https://publik.tuwien.ac.at/files/pub-et_3285.pdf}}</ref>