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:
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 a autoregressive time series of order greater than one.
Read more about this topic: Markov Process