LYAPUNOV FUNCTIONS FOR STOCHASTIC REACTION NETWORKS - DANIELE CAPPELLETTI - ETH ZURICH
Stochastic reaction networks are mathematical models used to describe the time evolution of chemical species counts. Despite their wide usage in active research areas such as natural and synthetic biology, epidemiology, and ecology, simple and relevant questions such as under what conditions a model converges to a stationary distribution are left unanswered. A typical strategy to study this issue makes use of the Foster-Lyapunov criteria introduced by Meyn and Teweedie. This approach is also encouraged by famous positive results in the deterministic modelling regime, which can be regarded to as a fluid limit of stochastic reaction networks: here, important stability results were obtained thanks to the study of Lyapunov functions (in the setting of ordinary differential equations). In his talk, Dr Cappelletti will give a brief overview of these methods and he will focus on recent results in the field. In particular, he will show how positive recurrence can be inferred for entire families of models, based on their graphical properties. He will then conclude by showing a novel computational framework to check for the existence of piecewise linear Foster-Lyapunov functions.
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