I was thinking of bringing some order into tags related to stochastic processes, namely Markov processes and Markov Chains. These are stochastic processes which admit Markov property. The trick is that there are 4 possible cases:
Discrete (i.e. countable) state space, discrete time.
General state space, discrete time.
Discrete state space, continuous time.
General state space, continuous time.
The point is that it is conventional to use Markov Chains for 1. and Markov process for 4. - but there are several opinions how to classify 2. and 3.
AMS classification classifies 2. as a Markov process - so Chain refer to the discrete space;
on the other hand, some authors e.g. Meyn, Tweedie and Revuz refer Chain to the discrete time;
I have already created markov-chains tag and I want to create markov-processes one since methods used for this problems are quite different. I agree with AMS classification in the sense that for me processes are on general spaces and chains are on discrete spaces - which is also reflected in methods. On the other hand since there are difference opinions I am not sure I have a right to create a tag's wiki saying that markov-chains refers to discrete space processes while markov-processes referes to process on the general state space. What would you advise?