Exponential convergence rates for stochastically ordered Markov processes under perturbation
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scl19.pdf
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Accepted version
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391.65 KB
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Author(s)
Gaudio, Julia
Amin, Saurabh
Jaillet, Patrick
Date Issued
September 2019
Journal
Systems & Control Letters
Publisher
Elsevier BV
Citation
Gaudio, Julia, Saurabh Amin, and Patrick Jaillet. "Exponential convergence rates for stochastically ordered Markov processes under perturbation." Systems & Control Letters, 133 (November 2019), 104515. © 2019 Elsevier B.V.
Version
Author's final manuscript
Abstract
In this technical note we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for stochastically ordered Markov processes starting from a fixed initial state, by allowing for a random initial condition that is also stochastically ordered. Our bounds are formulated in terms of moment-generating functions of hitting times. To illustrate our result, we find an explicit exponential convergence rate for an M/M/1 queue beginning in equilibrium and then experiencing a change in its arrival or departure rates, a setting which has not been studied to our knowledge.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.sysconle.2019.104515
