# Product Form Approximation of Transient Probabilities in Stochastic Reaction
Networks

### Abstract:

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.

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horvath
2011-09-12