# Math Help - Markov chaines periodic aperiodic

1. ## Markov chaines periodic aperiodic

How do we know whether they are periodic or aperiodic and how do we work out what is the periodicty.

Thanks.

2. Hello,

Have you read that : Markov chain - Wikipedia, the free encyclopedia ???

3. Im still confused

I have a matrix $\begin{array}{cccc}0.1&0.1&0&0.8\\0&0.9&0.1&0\\0&1 &0&0\\0.4&0&0&0.6\end{array}$

The classes are

{0} open
{1,2} closed
{3} open

How do i do periodicity, thanks for your help in advance.

4. a state is periodic if the probability of
returning to the state is zero except at regular intervals
eg if you go from 0 to 2 in a markov chain it should be the same number of steps to go from 2 to 0

5. Originally Posted by adam_leeds
Im still confused

I have a matrix $\begin{array}{cccc}0.1&0.1&0&0.8\\0&0.9&0.1&0\\0&1 &0&0\\0.4&0&0&0.6\end{array}$

The classes are

{0} open
{1,2} closed
{3} open

How do i do periodicity, thanks for your help in advance.
Hmmm draw a sketch with the arrows.
What do you call open and closed ? I know transient, absorbing and recurrent... (Markov chain - Wikipedia, the free encyclopedia)
And all are transient except 2, which is absorbing, because once you're in 2, you can't leave it since it returns to itself with probability 1.

Following from the criterion for the period of a chain, I'd advise you to consider i=2. And you should conclude with ease, it's not very hard