Exponential Convergence Rates for Stochastically Ordered Markov Processes with Random Initial Conditions

Julia Gaudio; Saurabh Amin; Patrick Jaillet

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arXiv · 1810.07732

Exponential Convergence Rates for Stochastically Ordered Markov Processes with Random Initial Conditions

Julia Gaudio·Saurabh Amin·Patrick Jaillet

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Abstract

In this brief paper 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.

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BibTeX RIS

Julia Gaudio, Saurabh Amin, Patrick Jaillet. 2018-10-17. Exponential Convergence Rates for Stochastically Ordered Markov Processes with Random Initial Conditions. https://arxiv.org/abs/1810.07732

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