Taylor series expansions for stationary Markov chains

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 ca...

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Bibliographic Details
Published in:Advances in applied probability 2003-12, Vol.35 (4), p.1046-1070
Main Authors: Heidergott, Bernd, Hordijk, Arie
Format: Article
Language:English
Subjects:
60J10
90C31
deviation matrix
Ergodic theory
General Applied Probability
Markov analysis
Markov chain
Markov chains
Markov processes
Mathematical differentiation
Mathematical functions
Mathematical models
measure-valued differentiation
Probability
Product rule
Radii of convergence
Series expansion
Studies
Sufficient conditions
Taylor series
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1239/aap/1067436334