Infinite Level-Dependent QBDs and Matrix Analytic Solutions for Stochastic Chemical Kinetics. Dayar, T., Sandmann, W., Spieler, D., & Wolf, V. Advances in Applied Probability, 2011.
Infinite Level-Dependent QBDs and Matrix Analytic Solutions for Stochastic Chemical Kinetics [link]Website  abstract   bibtex   
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.
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 title = {Infinite Level-Dependent QBDs and Matrix Analytic Solutions for Stochastic Chemical Kinetics},
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 year = {2011},
 volume = {43},
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 abstract = {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.},
 bibtype = {article},
 author = {Dayar, T and Sandmann, W and Spieler, D and Wolf, V},
 journal = {Advances in Applied Probability},
 number = {4}
}

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