Periodicity

If we denote the period of state  as , then it denotes the greatest common divisor (also known as HCF) of all integers  for which . In case , , then we define . For the case when the transition probability matrix is denoted by

, such that , then periodicity of each state is two (2). Now in case if due to some reason  for some , then periodicity of every state, , is one (1)
The periodicity of the following case, where the transition probability matrix is as given

 has the periodicity of each state as n.