Approximate Abstractions of Stochastic Hybrid Systems

This paper considers the issue of developing approximate abstractions of stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Our approach departs from the progress in stochastic reachability analysis and Markov chain approximations. For this purpose we have to introduce a new approximation scheme and look for a suitable metric. We construct an exponential timestepping approximation scheme for general Markov processes. This approximation scheme relies on the complex space of system trajectories involving a sensible choice of the metric. Fortunately, the Skorokhod metric is sly enough to overcome the problems.