LECTURE NOTES IN COMPUTER SCIENCE, VOL.10740, PP.312-316, 2018.

TITLE: A Software Tool for the Compact Solution of the Chemical 
Master Equation

AUTHORS: Tugrul Dayar and M. Can Orhan

ABSTRACT: The problem of computing the transient probability
distribution of countably infinite multidimensional 
continuous-time Markov chains (CTMCs) arising in systems of 
stochastic chemical kinetics is addressed by a software tool. 
Starting from an initial probability distribution, time 
evolution of the probability distribution associated with the 
CTMC is described by a system of linear first-order ordinary
differential equations, known as the chemical master equation 
(CME). The solver for the CME uses the time stepping implicit 
backward differentiation formulae (BDF). Solution vectors in 
BDF can be stored compactly during transient analysis in one 
of the Hierarchical Tucker Decomposition, Quantized Tensor 
Train, or Transposed Quantized Tensor Train formats.

KEY WORDS: Continuous-time Markov chain, chemical master 
equation, backward differentiation, compact vector, Kronecker 
decomposition.