Hi everyone

Can someone please help me with the following problem?

Let be independent and irreducible time-homogenous Markov Chains with common state-space E, and transition matrices P and Q respectively.

(a) Show that the two-dimentsional process defined by is a time-homogenous Markov chain with state space E E.

(b) Prove that if and are both periodic, then can be reducible.

(c) Show that is irreducible if both and are aperiodic.Hint:Use the fact that if is irreducible and aperiodic, then for each there exists some such that for all

Thanks,

bye bye