Any Stochastic Reaction Network has a Stationary Measure

In this note, we use a result by Harris (1957) to show that there always exists a stationary measure (not necessarily a distribution) on a closed irreducible component of a stochastic reaction network. This measure might not be unique. In particular, any weakly reversible stochastic reaction network has a stationary measure on all closed irreducibe components, irrespective whether it is compelx balanced or not.