Hybrid Limits of Continuous Time Markov Chains

We consider the behaviour of sequences of Continuous Time Markov Chains (CTMC) based models of systems of interacting entities, for increasing population levels, in situations when some transitions of the system have rates that are discontinuous functions. This can happen, for instance, in presence of guarded actions. In this setting, standard deterministic approximation results do not apply. However, one can still derive a differential equation by syntactic means, de facto defining an hybrid (piecewise-smooth) dynamical system. We prove that the sequence of CTMC converges to the trajectories of this hybrid dynamical system, under (mild) regularity conditions on these limit trajectories.