Speaker
Andrea Agazzi
(Bern University)
Description
We prove that, for weakly reversible chemical reaction networks with stochastic mass-action kinetics in two species, the associated continuous-time Markov chain is positive recurrent on each closed irreducible communicating class. Equivalently, the process returns to finite sets infinitely often with finite expected return times, and it possesses an invariant probability measure supported on the class.
The proof is based on a Foster–Lyapunov argument. Exploiting weak reversibility together with the geometric constraints of the two-dimensional state space, we construct a Lyapunov function allowing to establish, using pathwise large deviations estimates, sufficient asymptotic dissipation of the given process.
Author
Andrea Agazzi
(Bern University)
