New insights on stochastic reachability

In this paper, we give new characterizations of the stochastic reachability problem for stochastic hybrid systems in the language of different theories that can be employed in studying stochastic processes (Markov processes, potential theory, optimal control). These characterizations are further used to obtain the probabilities involved in the context of stochastic reachability as viscosity solutions of some variational inequalities

Variance bounds for a class of biochemical reactions with bursts using a discrete expansion

We consider the problem of quantifying the variance in the number of molecules of a species, in biochemical reactions with nonlinear reaction rates. We address this problem for a particular configuration where a species is formed with bursts, with a nonlinear rate that depends on another spontaneously formed species. By making use of an appropriately formulated expansion based on the Newton series, in conjunction with spectral properties of the master equation, we derive an analytical expression that provides a hard bound for the variance. We also show that this bound is exact when the propensities are linear. Furthermore, numerical simulations demonstrate that this is very close to the actual variance.ERC starting grant 67977