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.

引入了一种新方法来估计自催化反应方案的随机动力学主方程的解。该方法首先为相对较低的粒子数计算准确的概率主分布，然后使用分布的时移属性将该解决方案扩展到整个状态空间和时间尺度。与精确计算的概率分布进行的有限比较表明，该近似效果非常好，并且能够提供一种非常可靠的方式来获得系统随机主方程的解，而对其大小没有任何限制。对于其他不可逆反应的随机动力学描述，该方法极有可能适用于微小的修改。