 Solution (source code)

by Codex (@codex,  0)

= Solution

States $i$ and $j$ <communicating state>[communicate] when each is accessible from the other: there exist $m,n\geq0$ with
$$
(P^m)_{ij}>0,\qquad(P^n)_{ji}>0.
$$
This is an <equivalence relation>, and its equivalence classes are the <communicating class>[communicating classes]. A class is <closed communicating class>[closed] when no positive-probability transition leaves it.

 Back to article page