Explicit bounds for spectral theory of geometrically ergodic Markov kernels and applications

DOI10.3150/23-bej1609zbMath1530.60059OpenAlexW4307737106MaRDI QIDQ6178577

Loïc Hervé, James Ledoux

Publication date: 16 January 2024

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3150/23-bej1609

zbMATH Keywords

rate of convergencePoisson's equationsecond eigenvalueinvariant probability measuresmall setdrift conditionsperturbed Markov kernels

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Approximations to statistical distributions (nonasymptotic) (62E17)

Cites Work

• Geometric ergodicity for classes of homogeneous Markov chains
• Markov chains and stochastic stability
• General state space Markov chains and MCMC algorithms
• Generalization of a fundamental matrix
• Computable bounds for geometric convergence rates of Markov chains
• Geometric ergodicity and hybrid Markov chains
• Essential spectral radius for Markov semigroups. I: Discrete time case
• Perturbation theory for Markov chains via Wasserstein distance
• Large deviations asymptotics and the spectral theory of multiplicatively regular Markov proces\-ses
• Renewal theory and computable convergence rates for geometrically erdgodic Markov chains
• Spectral theory and limit theorems for geometrically ergodic Markov processes
• Perturbation bounds for Monte Carlo within metropolis via restricted approximations
• \(V\)-geometrical ergodicity of Markov kernels via finite-rank approximations
• On the limitations of single-step drift and minorization in Markov chain convergence analysis
• Convergence rate of the powers of an operator. Applications to stochastic systems
• Approximating Markov chains and \(V\)-geometric ergodicity via weak perturbation theory
• A Liapounov bound for solutions of the Poisson equation
• Quasi-compactness and absolutely continuous kernels
• Spectral Analysis of Markov Kernels and Application to the Convergence Rate Of Discrete Random Walks
• Markov Chains and Stochastic Stability
• Inequalities in Theorems of Ergodicity and Stability for Markov Chains with Common Phase Space. II
• Truncation approximations of invariant measures for Markov chains
• A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations
• Markov Chains
• Regular Perturbation of V-Geometrically Ergodic Markov Chains
• Error bounds for augmented truncation approximations of Markov chains via the perturbation method
• Sur un Theoreme Spectral et son Application aux Noyaux Lipchitziens
• On the geometric ergodicity of Metropolis-Hastings algorithms
• Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
• Robustness of iterated function systems of Lipschitz maps

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