January 1, 2026PeriodicityPeriodicity ($d(i)$)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.RelatedSTA447Class PropertyAperiodicityn-Step Transition ProbabilityCommunication ClassCourse Notes