On sequential compactness of solutions for a class of stochastic hybrid systems

This work presents a summary of new results on sequential compactness of solutions for a class of stochastic hybrid systems. The main result is that every almost surely locally eventually bounded sequence of solutions with given statistical properties admits a solution in its pointwise outer limit with similar statistical properties. Moreover, if a sequence is not locally eventually bounded in probability then the system must exhibit finite escape times. Applications of these results to robust reachability and stability theory are also presented.