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Infinite level-dependent QBD processes and matrix-analytic solutions for stochastic chemical kinetics

Part of:Physiological, cellular and medical topicsMarkov processes

Published online by Cambridge University Press:  01 July 2016

Tuğrul Dayar,
Werner Sandmann,
David Spieler and
Verena Wolf
Tuğrul Dayar*
Affiliation:
Bilkent University
Werner Sandmann*
Affiliation:
Clausthal University of Technology
David Spieler*
Affiliation:
Saarland University
Verena Wolf*
Affiliation:
Saarland University
*
∗ Postal address: Department of Computer Engineering, Bilkent University, TR-06800 Bilkent, Ankara, Turkey.
∗∗ Postal address: Department of Applied Stochastics and Operations Research, Clausthal University of Technology, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany. Email address: werner.sandmann@tu-clausthal.de
∗∗∗ Postal address: Faculty of Computer Science, Saarland University, D-66123 Saarbrücken, Germany.
∗∗∗ Postal address: Faculty of Computer Science, Saarland University, D-66123 Saarbrücken, Germany.
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Abstract

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Systems of stochastic chemical kinetics are modeled as infinite level-dependent quasi-birth-and-death (LDQBD) processes. For these systems, in contrast to many other applications, levels have an increasing number of states as the level number increases and the probability mass may reside arbitrarily far away from lower levels. Ideas from Lyapunov theory are combined with existing matrix-analytic formulations to obtain accurate approximations to the stationary probability distribution when the infinite LDQBD process is ergodic. Results of numerical experiments on a set of problems are provided.

Keywords

Stochastic chemical kineticslevel-dependent quasi-birth-and-death processstate space truncationLyapunov boundmatrix-analytic solution

MSC classification

Primary:60J22: Computational methods in Markov chains
Secondary:60J28: Applications of continuous-time Markov processes on discrete state spaces92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)92D25: Population dynamics (general)

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011, pp. 1005 - 1026
Copyright
Copyright © Applied Probability Trust 2011 

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