Product Form Approximation of Transient Probabilities in Stochastic Reaction Networks

Most Markov chains that describe networks of stochastic reactions have a huge state space. This makes exact analysis infeasible and hence the only viable approach, apart from simulation, is approximation. In this paper we derive a product form approximation for the transient probabilities of such Markov chains. The approximation can be interpreted as a set of interacting time inhomogeneous Markov chains with one chain for every reactant of the system. Consequently, the computational complexity grows only linearly in the number of reactants and the approximation can be carried out for Markov chains with huge state spaces. Several numerical examples are presented to illustrate the approach.