A novel method is introduced to estimate the solution of the stochastic kinetic master equation of an autocatalytic reaction scheme. The method first computes an accurate probability master distribution for relatively low particle numbers, then uses a time shift property of the distributions to extend this solution to the entire state space and time scale. A limited comparison with accurately calculated probability distributions suggests that the approximation works exceptionally well and is able to provide a very reliable way to obtain the solution of the stochastic master equation of a system without any limitation on its size. The method will most probably be applicable with minor modifications for the stochastic kinetic description of other irreversible reactions as well. (C) 2016 Elsevier Ltd. All rights reserved.