Date of Completion
The goal of this work is threefold. Firstly, we review some general notions and results related to couplings of discrete-time Markov chains focusing on qualitative criteria which help determine whether a given coupling provides sharp bounds. Secondly, we highlight the notion of greedy couplings, those maximizing the probability of meeting in the next step, and thirdly we provide an exhaustive study of greedy couplings for the simple yet not entirely trivial setting of three state chains.
DiCicco, Mason and Ben-Ari, Iddo, "Greedy Coupling of 3-State Markov Chains" (2020). Honors Scholar Theses. 709.