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