Do 2 Markov chains $\left\{X_n\right\}^\inf_{n=0} $ and $\left\{Y_n\right\}^\inf_{n=0} $ with all of these properties exist so that the probability for infinite n values to maintain $X_n=Y_n$ is 0? is 1? is 0.5?
- same group of states
- same transition matrix
- different starting states
I was thinking that for the probability to be 1 all the values in the transition matrix must be equal.
For the probability to be 0 all the values in the transition matrix must be different. But since we're talking about infinite number of N values, how can I illustrate this? Or maybe I'm going about this the wrong way?