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Taylor series expansions for stationary Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Bernd Heidergott  and
Arie Hordijk
Bernd Heidergott*
Affiliation:
Vrije Universiteit Amsterdam and Tinbergen Institute
Arie Hordijk*
Affiliation:
Leiden University
*
∗ Postal address: Vrije Universiteit Amsterdam, Department of Economics, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Email address: [email protected]
∗∗ Postal address: Leiden University, Mathematical Institute, PO Box 9512, 2300 RA Leiden, The Netherlands.
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Abstract

We study Taylor series expansions of stationary characteristics of general-state-space Markov chains. The elements of the Taylor series are explicitly calculated and a lower bound for the radius of convergence of the Taylor series is established. The analysis provided in this paper applies to the case where the stationary characteristic is given through an unbounded sample performance function such as the second moment of the stationary waiting time in a queueing system.

Keywords

Markov chainTaylor seriesmeasure-valued differentiationdeviation matrix

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 90C31: Sensitivity, stability, parametric optimization
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 1046 - 1070
Copyright
Copyright © Applied Probability Trust 2003 

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