A note on faithful coupling of Markov chains

Debojyoti Dey, Pranjal Dutta, Somenath Biswas

One often needs to turn a coupling $(X_i,Y_i{)}_{i\ge 0}$ of a Markov chain into a sticky coupling where once $X_T=Y_T$ at some $T$, then from then on, at each subsequent time st…