KSMB-SMB 2024 Seoul

Stochastic reaction networks with time-varying rates

Stochastic reaction networks are typically used as models in biochemistry. In their classical definition, the rates at which chemical reactions occur only depend on the current state. However this is not true in many biological systems, where the rate values at a given state fluctuate over time. I will present some models where the rates depend on both the current configuration and another stochastic process, which is not directly affected by the system of interest. I will focus on the study of the positive recurrence of this more general model under the assumption of “monomolecularity”. Here, under certain conditions, the stationary distribution exists and is a mixture of Poisson distributions, uniquely identified as the law of a fixed point of a stochastic recurrence equation. I will further show some results on models with rates that randomly switch between different fixed values.