states = {1,2,3,4}
I'm confused if the following markov chain is irreducible or not. I think it's not irreducible because if it reaches from one state to another with probability 1 it stays there. I think it's not aperiodic as there are no self loops.
Asked
Active
Viewed 171 times
-2
noname
- 27
1 Answers
0
It sends a variable from state 1 -> 2 -> 3 -> 4 -> 1. So it is periodic with period 4. In this case it is also irreducible.
Martini
- 39
-
Thank you for your answer, I just have another question how do i show P^(n) is equal to 1/4 as the limit approaches infinity. The stationary distribution is given which is (1/4, 1/4, 1/4, 1/4) – noname Mar 28 '23 at 21:39
-
Do you mean when the limit of n goes to infinity? For your understanding, P^(n) is this matrix/markov chain applied to your input n times, note P^1 = P^4 since it is 4 periodic. It is itself another matrix, so it cannot be equal to one number. – Martini Mar 28 '23 at 22:57