We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of the Markov processes and calculations of stationary distributions. Since the class of processes expressible through such networks is big and only few assumptions are made, the principle also applies to other stochastic models. We give examples of interest from CRN theory to highlight the decomposition.

我们通过相关的连续时间马尔可夫过程检查反应网络 (CRN)。研究此类网络的动力学通常很难，无论是通过分析还是通过模拟。特别是，随机反应网络的平稳分布仅在某些情况下是已知的。我们在join操作下分析了CRN的底层连续时间马尔可夫链的类属性，并检查了CRN的平稳分布的形式来自分解的CRN的部分的条件。可以在示例中轻松检查条件并允许递归应用。所开发的理论能够实现马尔可夫过程的顺序分解和平稳分布的计算。由于通过此类网络可表达的过程类别很大，并且只进行了很少的假设，该原则也适用于其他随机模型。我们给出了 CRN 理论中感兴趣的例子来强调分解。