Definition

$i \to j \Leftrightarrow \exists T_{0} \in N_{0} : p_{ij}^{(T_{0})} > 0$

$\forall i, j \in E$ , $j$ is accessible from $i$

where ${X_{t}}$ is a HMC defined on the state space $E$ and the $P$ is a transition matrix of ${X_{t}}$ and $p_{ij}^{(T_{0})}$ is a $(i, j)$ -th element of $P^{T_{0}}$