Advances in Applied Probability

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

Tugrul Dayar, Werner Sandmann, David Spieler, and Verena Wolf

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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.

Article information

Adv. in Appl. Probab., Volume 43, Number 4 (2011), 1005-1026.

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30] 92D25: Population dynamics (general)

Stochastic chemical kinetics level-dependent quasi-birth-and-death process state space truncation Lyapunov bound matrix-analytic solution


Dayar, Tugrul; Sandmann, Werner; Spieler, David; Wolf, Verena. Infinite level-dependent QBD processes and matrix-analytic solutions for stochastic chemical kinetics. Adv. in Appl. Probab. 43 (2011), no. 4, 1005--1026. doi:10.1239/aap/1324045696.

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