Any general stochastic process can be made to satisfy the Markov property by altering the state space (and adding probabilities for any new states). In this way, it can "turn into" a Markov chain. Given a stochastic process with state space $S$, which of the following methods would create a Markov chain that models the same process?

1. Alter $S$to instead contain sequences of states, the $k^\text{th}$element of which tells where the Markov chain was at step $k$.
2. Change $S$to contain pairs of states $(i, \, j)$instead. That way, the Markov chain can know both the present state and the previous state.
3. Modify $S$to contain only one state, but make its transition probabilities contain all the information about the stochastic process.
4. Don't change $S$, but make the transition probabilities satisfy the Markov property.
5. Add a large number of "in-between" states to $S$, to create a bunch of little steps satisfying the Markov property.