Reference no: EM132857574

For each of the following, give an example of a Markov chain with the desired properties. You may exhibit the chain in any way that makes the example clear (eg. giving the transition matrix, giving the transition state diagram with edges labeled, declaring it to be a random walk on a given graph). You may use examples more than once.

1. An irreducible but not ergodic Markov chain.

2. An aperiodic but not irreducible Markov chain.

3. An ergodic Markov chain.

4. A Markov chain with a unique stationary distribution but no limiting distribution.

5. A 3-state Markov chain with infinitely many stationary distributions.