The ODE method for stability of skip-free Markov chains with applications to MCMC

DOI10.1214/07-AAP471zbMath1148.60052arXivmath/0607800OpenAlexW2075010686MaRDI QIDQ2426609

Pierre Priouret, Eric Moulines, Gersende Fort, Sean P. Meyn

Publication date: 23 April 2008

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607800

zbMATH Keywords

Markov chainfluid limitsubgeometric ergodicityskip-free chain

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Monte Carlo methods (65C05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (3)

The ODE method for stability of skip-free Markov chains with applications to MCMC ⋮ Stability of Multi-Dimensional Birth-and-Death Processes with State-Dependent 0-Homogeneous Jumps ⋮ Analysis of non-reversible Markov chains via similarity orbits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov chains and stochastic stability
• The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory
• Criterion for ergodicity of homogeneous discrete Markov chains
• On exponential ergodicity of multiclass queueing networks
• A multivariate mixture of Weibull distributions in reliability modeling.
• Discretization and MCMC. Convergence assessment
• State-dependent criteria for convergence of Markov chains
• Stability and instability of a two-station queueing network
• Brownian models of open processing networks: Canonical representation of workload.
• Networks and queues: Probabilistic methods
• Geometric ergodicity of Metropolis algorithms
• Value iteration and optimization of multiclass queueing networks
• Performance evaluation and policy selection in multiclass networks
• Practical drift conditions for subgeometric rates of convergence.
• On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models
• Transience of multiclass queueing networks via fluid limit models
• The ODE method for stability of skip-free Markov chains with applications to MCMC
• Large deviation asymptotics and control variates for simulating large functions
• A Liapounov bound for solutions of the Poisson equation
• A fluid limit model criterion for instability of multiclass queueing networks
• Instability in stochastic and fluid queueing networks
• Polynomial ergodicity of Markov transition kernels.
• Sequencing and Routing in Multiclass Queueing Networks Part I: Feedback Regulation
• Stochastic-Process Limits
• A calculus for network delay. II. Network analysis
• Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
• Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations
• Subgeometric Rates of Convergence of f-Ergodic Markov Chains
• Stability and convergence of moments for multiclass queueing networks via fluid limit models
• Stability and Instability of Fluid Models for Reentrant Lines
• Workload models for stochastic networks: value functions and performance evaluation
• Control Techniques for Complex Networks
• Solutions of ordinary differential equations as limits of pure jump markov processes
• Some Multivariate Chebyshev Inequalities with Extensions to Continuous Parameter Processes

This page was built for publication: The ODE method for stability of skip-free Markov chains with applications to MCMC