Periodicity ($d(i)$)

  • Definition: The period of state $i$ is the greatest common divisor of all step counts $n \ge 1$ such that $P_{ii}^{(n)} > 0$.
  • Formula:
$$ d(i)=\gcd\{n\ge 1: P_{ii}^{(n)} > 0\}. $$
  • Property Mapping: Periodicity is a class property.