Series Expansions for Continuous-Time Markov Processes

Bernd Heidergott (), Arie Hordijk () and Nicole Leder ()
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Bernd Heidergott: Department of Econometrics, Vrije Universiteit Amsterdam, and Tinbergen Institute, 1081 HV Amsterdam, The Netherlands
Arie Hordijk: Mathematical Institute, Leiden University, 2300 RA Leiden, The Netherlands
Nicole Leder: Department of Mathematics, University of Hamburg, 20146 Hamburg, Germany

Operations Research, 2010, vol. 58, issue 3, 756-767

Abstract: We present update formulas that allow us to express the stationary distribution of a continuous-time Markov process with denumerable state space having generator matrix Q * through a continuous-time Markov process with generator matrix Q . Under suitable stability conditions, numerical approximations can be derived from the update formulas, and we show that the algorithms converge at a geometric rate. Applications to sensitivity analysis and bounds on perturbations are discussed as well. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

Keywords: probability; Markov processes; queues; algorithms; numerical methods; retrial queue; deviation matrix; sensitivity analysis (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:58:y:2010:i:3:p:756-767

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