# Tags: Markov process and Markov Chains

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:

1. Discrete (i.e. countable) state space, discrete time.

2. General state space, discrete time.

3. Discrete state space, continuous time.

4. 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 tag and I want to create 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 refers to discrete space processes while referes to process on the general state space. What would you advise?

• FWIW, since Wikipedia has become the de facto first source for fact checking, it does refer to "Often, the term Markov chain is used to mean a Markov process which has a discrete (finite or countable) state-space." Just for clarification, is it true in your experience that the different methods used usually corresponds to discrete versus continuous state space (as oppose to discrete versus continuous time)? – Willie Wong Apr 2 '12 at 6:46
• @Willie: thanks for the advise! Well, at least it is my impression that the discrete space there is much more important that the continuous time because of the topology - you just consider transition between points rather than between sets. – Ilya Apr 2 '12 at 10:01
• I edited your tag wiki contributions a bit (the mouse over text doesn't display the whole wiki excerpt, so I shortened the description so that the sentence disambiguating (markov-chains) and (markov-process) will be shown.) – Willie Wong Apr 2 '12 at 12:44
• @WillieWong: thank you very much, I have also created a markov-process wiki. Do you think I should make it shorter? – Ilya Apr 2 '12 at 12:47