Subexponential Upper and Lower Bounds in Wasserstein Distance for Markov Processes

Nikola Sandrić, Ari Arapostathis, Guodong Pang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this article, relying on Foster–Lyapunov drift conditions, we establish subexponential upper and lower bounds on the rate of convergence in the L p-Wasserstein distance for a class of irreducible and aperiodic Markov processes. We further discuss these results in the context of Markov Lévy-type processes. In the lack of irreducibility and/or aperiodicity properties, we obtain exponential ergodicity in the L p-Wasserstein distance for a class of Itô processes under an asymptotic flatness (uniform dissipativity) assumption. Lastly, applications of these results to specific processes are presented, including Langevin tempered diffusion processes, piecewise Ornstein–Uhlenbeck processes with jumps under constant and stationary Markov controls, and backward recurrence time chains, for which we provide a sharp characterization of the rate of convergence via matching upper and lower bounds.

Original languageEnglish (US)
Article number24
JournalApplied Mathematics and Optimization
Volume85
Issue number3
DOIs
StatePublished - Jun 2022

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Subexponential Upper and Lower Bounds in Wasserstein Distance for Markov Processes'. Together they form a unique fingerprint.

Cite this