Short Communications

Mallows distance convergence for heavy-tailed Markov chains: regeneration approach

M. L. Calvache-Hoyos^a, C. C. Y. Dorea^b, E. S. Silva^c, W. M. Soares<sup>d

a</sup> Universidade Federal de Sergipe, Brazil
^b Universidade de Brasilia, Brazil
^c Secretaria de Estado da Educação da Bahia, Brazil
^d Instituto Federal de Brasilia, Brazil

Abstract: 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.

Keywords: Mallows distance, stable laws, Markov chains, regeneration.

Received: 14.05.2024
Accepted: 06.02.2025

DOI: 10.4213/tvp5722

 English version: Theory of Probability and its Applications, 2025, 70:3, 432–439

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