To my (basic) understanding a Markov process is a process wherein the future state of a system only depends on the current state, and not on the past states of the system.
I was wondering on what the standard approach is on systems that inherently hold information about their past in them.
One could image, in the discrete-time case, system carrying in it a representation of it's three previous states. There are two cases to distinguish here:
- The future state of the system is not a function of this memory and only of factors that don't have anything to do with it. This is perhaps a boring case (although there might be interesting examples I don't know of).
- The future state of the system is a function of this memory information, yet in a "Markovian" way. This is the case I am most interested in.
Are these things that would be considered as Markovian systems (perhaps on a different scale)? Are there examples of these kinds of systems?