Its the number of steps a state takes to get return back to itself...which is 1)Obviously greater than 1 2)is a multiple of any no d,where d >1. for example if its d=2 then after each 2,4,6,8...steps the given state will return back to itself . And if these conditions are satisfied,then its periodic otherwise its aperiodic.
It's important to realise that periodic is where a return from a state to itself is ONLY possible in a multiple of k>1 steps. If a Markov chain is irreducible and one of the states has a period of k, this means all the states have a period of k Good luck! John
