Let and , , be two discrete-time Markov chains such that , for all . Let be a non-negative random variable in (T may depend on X and Y).
Is it true that ?
Thanks, you're right, after conditioning we found that that is true.
My only concern was that with martingales, for a stopping time T, it is not true that its expectation is zero at T (which is random) even though is zero for all fixed t>0... This does not apply in my case maybe. I have to study more theory.