Given a Markov chain on an infinite and countable set of states, with one irreductible class that has a finite number of states, why can its transition matrix be put in a lower triangular form ?
$\begin{bmatrix}D & 0\\R & Q\end{bmatrix}$
And then, why is its asymptotic behavior not unique?
I would be very grateful if people could direct me to a good book that discusses the behavior of Markov chains based on the structure of their transition matrix :)
Cheers