An <irreducible Markov chain> has the property that for every pair of states $i,j$ there is an integer $n\geq0$ with $(P^n)_{ij}>0$. Equivalently every state can reach every other state along a finite path of positive-<probability> transitions.

Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / ib / Paper 1 / 11H / a / Solution

 Solution (source code)