Robust global recurrence for a class of stochastic hybrid systems

We study a weak property called recurrence for a class of stochastic hybrid systems and establish robustness of the recurrence property. In particular, we establish that recurrence of an open, bounded set is robust to sufficiently small perturbations in the set, perturbations of the data of the stochastic hybrid system and modifications to the system data that slow down the recurrence property. The robustness results are a consequence of the mild regularity properties assumed for the stochastic hybrid system.