Stochastic reaction networks are mathematical models heavily utilized in biochemistry. Usually, it is assumed the rates at which biochemical transformations occur only depend on the current chemical configuration. Motivated by biological applications, in this study my collaborators and I considered the more general case of the rates depending on both the current configuration and another stochastic process (which we call "stochastic environment"). In order to study the transient and stationary behavior of this more complex model, it is not sufficient to average the effect of the environment over time, and I will show this via examples. I will then show that, under certain conditions, the stationary distribution of the model exists and it can be characterized as the mixture of Poisson distributions solving a specific stochastic recurrence equation. This recursion can be utilized for the statistical computation of moments and other distributional features.
Meet link: https://meet.google.com/bgt-oqys-gme