Suppose I have a transition matrix (A) for a Markov chain.
Now suppose there’s a second transition matrix (B) for another Markov chain over the same states.
Now suppose I alternate between the two Markov chains, so that essentially I’m doing the matrix multiplication A x B x A x B … indefinitely.
Is there anything I can say about the product of these two transition matrices (I.e. A x B)? Ideally information on the stationary distribution when we have the alternating Markov chain structure or some other repeating sequence of the form A^m x B^n would be interesting…