Mallows Distance Convergence for Heavy-Tailed Markov Chains: Regeneration Approach

For heavy-tailed Markov chains we derive conditions for the convergence in Mallows distance. We make use of a concept of Mallows distance (also known as the Wasserstein distance) between regenerative sequences. The novelty of our approach is in the use of regenerative processes, which is a probability technique capable of splitting a Markov chain into independent and identically distributed cycles for analysis of asymptotic behavior, including aperiodic and recurrent regenerative processes.