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Empirical convergence rates for continuous-time Markov chains

Part of: Markov processes Special processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Geoffrey Pritchard  and
David J. Scott
Geoffrey Pritchard*
Affiliation:
University of Auckland
David J. Scott*
Affiliation:
University of Auckland
*
∗ Postal address: Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand.
∗∗ Email address: g.pritchard@auckland.ac.nz
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Abstract

We consider the problem of estimating the rate of convergence to stationarity of a continuous-time, finite-state Markov chain. This is done via an estimator of the second-largest eigenvalue of the transition matrix, which in turn is based on conventional inference in a parametric model. We obtain a limiting distribution for the eigenvalue estimator. As an example we treat an M/M/c/c queue, and show that the method allows us to estimate the time to stationarity τ within a time comparable to τ.

Keywords

continuous-time Markov chaineigenvalueconvergence rateM/M/c/c queuerandom matrix

MSC classification

Primary: 62M05: Markov processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 262 - 269
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

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