> All systems can be represented as a pair of functions that map current state to next state and the observation of current state, in response to some perturbation.
If you are assuming the next state depends on the current state, doesn't this work for only Markov system i.e where you can make predictions for the future based solely on its present state?
There's a whole bunch of systems where this doesn't apply, no?
No, because a Markov process only depends on current state. All Markov processes are stateful systems, but not all stateful systems are Markov processes.
For example, an exponential moving average:
s_n+1 = a x_n + (1 - a) s_n
y_n = s_n
where a, x, s, y in Reals
The next state depends on all past state, including initial conditions.
Conceptually, stateful systems are the notion "where I am going depends on where I am." Markov processes are stateful systems where "where I am going depends on where I am, but not upon where I came from."
If you are assuming the next state depends on the current state, doesn't this work for only Markov system i.e where you can make predictions for the future based solely on its present state?
There's a whole bunch of systems where this doesn't apply, no?