Editing Coupling (probability) (section)

=== Convergence of Markov Chains to a stationary distribution ===
Initialize one process <math>X_n</math> outside the stationary distribution and initialize another process <math> Y_n </math> inside the stationary distribution. Couple these two independent processes together <math> (X_n,Y_n) </math>. As you let time run these two processes will evolve independently. Under certain conditions, these two processes will eventually meet and can be considered the same process at that point. This means that the process outside the stationary distribution converges to the stationary distribution.