Advances in Applied Probability

Taylor series expansions for stationary Markov chains

Bernd Heidergott and Arie Hordijk

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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.

Article information

Adv. in Appl. Probab. Volume 35, Number 4 (2003), 1046-1070.

First available in Project Euclid: 29 October 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 90C31: Sensitivity, stability, parametric optimization

Markov chain Taylor series measure-valued differentiation deviation matrix


Heidergott, Bernd; Hordijk, Arie. Taylor series expansions for stationary Markov chains. Adv. in Appl. Probab. 35 (2003), no. 4, 1046--1070. doi:10.1239/aap/1067436334.

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