Period of a state in a Markov chain
= Period of a state in a Markov chain
{title2=$d(i)$}
The period of a state $i$ is the greatest common divisor of its positive-probability return times:
$$
d(i)=\gcd\{n\geq1:P^n(i,i)>0\}.
$$
A state is aperiodic when its period is one.