Accessible State

Definition

A state $j$ is said to be accessible from state $i$ if:

$P_{ij}^n>0\text{for some }n\ge 0$

Notation: $i\to j$

Interpretation

Starting from state $i$, it is possible to eventually enter state $j$.

Non-Accessibility

If $j$ is not accessible from $i$, then:

$P\{\text{ever enter }j\mid \text{start in }i\}={\sum }_{n=0}^{\infty }{P}_{ij}^n=0$

Related

• Communication
• Communicating Classes
• Irreducible