Stationary distributions via decomposition of stochastic reaction networks

Linard Hoessly

Published 2019-10-07Version 1

Despite their importance, stationary distributions of stochastic reaction networks (CRNs) are only known in few 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 CRNs and calculations of stationary distributions. We give examples of interest from CRN theory to highlight the decomposition.