Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let's say a Markov chain has the state-space $S = \{A,B,C,D\}$ Transition Matrix as follows:

$$ \begin{bmatrix} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \end{bmatrix} $$

This is NOT irreducible as far as I am aware due to state C being transient.

To find an equilibrium distribution for the chain, would I just treat it the same way as if it were irreducible in which case I get $\pi = (1/3)(1,1,0,1)$. Is this unique? I'm not sure. Thanks in advance!

share|improve this question

1 Answer 1

This Markov chain is periodic, so no stationary distribution exists. If we start in state A we see the pattern ADBADBADB... so we know every third time step we will be in either A, D or B. And if we start the chain in state C then the pattern is CADBADBADB...

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.