Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions

DOI10.1214/21-AIHP1195zbMath1494.60077arXiv1902.02964OpenAlexW2947437263MaRDI QIDQ2155517

Qian Qin, James P. Hobert

Publication date: 15 July 2022

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.02964

zbMATH Keywords

convergence analysisexponential convergencePolish spaceKantorovich-Rubinstein distancequantitative boundLyapunov drift function

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (5)

Strict Kantorovich contractions for Markov chains and Euler schemes with general noise ⋮ Geometric ergodicity in a weighted Sobolev space ⋮ Spectral telescope: convergence rate bounds for random-scan Gibbs samplers based on a hierarchical structure ⋮ Exact convergence analysis for metropolis–hastings independence samplers in Wasserstein distances ⋮ Convergence rate bounds for iterative random functions using one-shot coupling

Cites Work

• Unnamed Item
• Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
• Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors
• Locally contractive iterated function systems
• Existence and application of optimal Markovian coupling with respect to non-negative lower semi-continuous functions
• Practical drift conditions for subgeometric rates of convergence.
• Wasserstein-based methods for convergence complexity analysis of MCMC with applications
• Subgeometric rates of convergence of Markov processes in the Wasserstein metric
• Quantitative contraction rates for Markov chains on general state spaces
• Locally contracting iterated functions and stability of Markov chains
• Geometric L² and ^{L1 convergence are equivalent for reversible Markov chains}
• General Irreducible Markov Chains and Non-Negative Operators
• Markov Chains
• Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
• Optimal Transport
• Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

This page was built for publication: Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions