Assuming an irreducible, positive recurrent Markov Pure jump markov process with state space, $S={0,1}$
The embedded Markov Chain which is doubly stochastic (i.e) columns and rows of the transition matrix sum up to 1.
Find the steady state distribution (SSD).
I know that for a Markov chain that has a doubly stochastic transition matrix will have the uniform distribution as the SSD. In other words, 1/(number of states in the state space).
I could solve for the SSD by solving $\pi q=0$, where q is the generator.Since the answer is not just 1/(number of states in the state space), would like to ask why does it differ? and is there a way to relate them both?
Thanks heaps!