Strict Kantorovich contractions for Markov chains and Euler schemes with general noise

Lu-Jing Huang, Mateusz B. Majka, Jian Wang

Research output: Contribution to journalArticlepeer-review

Abstract

We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the standard Lp-Wasserstein distances for p≥1. We present explicit lower bounds of the corresponding contraction rates. By employing the refined basic coupling and the coupling by reflection, the results are applied to Markov chains whose transitions include additive stochastic noises that are not necessarily isotropic. This can be useful in the study of Euler schemes for SDEs driven by Lévy noises. In particular, motivated by recent works on the use of heavy tailed processes in Markov Chain Monte Carlo, we show that chains driven by the α-stable noise can have better contraction rates than corresponding chains driven by the Gaussian noise, due to the heavy tails of the α-stable distribution.
Original languageEnglish
Pages (from-to)307-341
Number of pages35
JournalStochastic Processes and their Applications
Volume151
Early online date17 Jun 2022
DOIs
Publication statusPublished - Sep 2022

Keywords

  • Coupling by reflection
  • Markov chain
  • Refined basic coupling
  • Strict Kantorovich contractivity
  • Total variation
  • Wasserstein distance

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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