On the numerical solution of the chemical master equation with sums of rank one tensors

Abstract

We show that sums of rank one tensors (or separable functions) representing the so-called Candecomp/Parafac or cp-decomposition is used effectively to solve the chemical master equations as in many cases the effective tensor rank of the probability distribution only grows slowly with time. Both theoretical bounds and computational experiments are presented which support this claim. The proposed numerical algorithm is thought to provide an effective tool for the computational study of stochastic biochemical systems involving large numbers of different chemical species.