Exponential convergence rates for stochastically ordered Markov processes under perturbation
Author(s)Gaudio, Julia; Amin, Saurabh; Jaillet, Patrick
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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.
DepartmentMassachusetts 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
Systems & Control Letters
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.
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