Computable exponential convergence rates for stochastically ordered Markov processes

DOI10.1214/aoap/1034968072zbMath0863.60093OpenAlexW2075313566MaRDI QIDQ1921439

Robert B. Lund, Sean P. Meyn, Richard L. Tweedie

Publication date: 10 June 1997

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

Full work available at URL: https://doi.org/10.1214/aoap/1034968072

zbMATH Keywords

total variationtandem queuescouplingexponential ergodicityreflected diffusionsdrift functionsdam processes

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Queueing theory (aspects of probability theory) (60K25)

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Cites Work

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• Calculation of the Laplace transform of the length of the busy period for the M/G/1 queue via martingales
• Stochastic monotonicity and queueing applications of birth-death processes
• Stochastic inequalities on partially ordered spaces
• Stability of generalized Jackson networks
• Ergodicity of Jackson-type queueing networks
• Exponential and uniform ergodicity of Markov processes
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• The coupling of regenerative processes
• Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process
• Transient behavior of regulated Brownian motion, I: Starting at the origin
• Exponential ergodicity in Markovian queueing and dam models
• Storage processes with general release rule and additive inputs
• Some estimates of the rate of convergence for birth and death processes
• Useful martingales for stochastic storage processes with Lévy input
• The exponential rate of convergence of the distribution of the maximum of a random walk
• A classification of the second order degenerate elliptic operators and its probabilistic characterization
• The exponential rate of convergence of the distribution of the maximum of a random walk. Part II
• Stochastic monotonicity in general queueing networks
• A Dam with seasonal input
• A comparison of convergence rates for three models in the theory of dams
• Geometric Convergence Rates for Stochastically Ordered Markov Chains
• Complete exponential convergence and some related topics