5th Italian Meeting on Probability and Mathematical Statistics

Stability of Reaction Networks with Randomly Switching Parameters - part 1

Stochastic chemical reaction network dynamics (co-organized with Lucie Laurence)

Since the dawn of stochastic chemical reaction network theory over 50 years ago, there have been many general results about (positive) recurrence, especially in the case of mass-action kinetics. One less-explored area is that of mass-action models whose rate constants, rather than being static, are themselves stochastic. Such models have relevance in applications, since biomolecular systems rarely exist in isolation and their rates often depend on time-changing quantities. In this series of two talks, we will study the stability of such models under some linearity assumptions. In this first talk, I will present structural conditions implying positive recurrence, regardless of the specific choice of parameters of the model. I will further present an algebraic characterization of the stationary distribution in terms of a stochastic recurrence equation, which can be exploited to numerically calculate the conditional stationary distribution and its moments.