ADVANCES IN APPLIED PROBABILITY, VOL.43, PP.1005-1026, 2011.  

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

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

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 is ergodic. Results of numerical experiments on a set of problems are 
provided.   

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