Markov chains: period of a state

[mmarkov]

Hello,

I am trying to understand the intuition of the definition of the period of a state in a Markov chain.

Say for example we can go from state i to state i in 3,5,7,9,11... and so on steps.
The gcd here is one. So is this aperiodic state or one with periodicity of 2.

Thanks

 

[WWGD]

What gcd are you referring to? gcd(3,15)=3. I see, it is the gcd of all states of "return". Assume the gcd is k. (assume for simplicity k is prime ).Then the state repeats at stages k,2k, ... This is pretty well explained in Wikipedia, or here : http://stats.stackexchange.com/ques...-explanation-for-periodicity-in-markov-chains