In this talk we will discuss the notion of fluid limit of a sequence of stochastic processes from a more "computer-scientific" point of view. We will start from an high level modelling language, define different semantics of this language, in terms of CTMC, ODE and hybrid systems, and then investigate the relationships between these semantics. In addition to classical fluid theorems, emerging while considering CTMC and ODE semantics, two other cases are interesting:
1. Convergence results of a sequence of CTMC to an hybrid system, integrating discrete+stochastic and continuous dynamics;
2. Convergence results in the presence of discontinuities, caused by guarded transitions in the high level model. In this case, we will show convergence of a sequence of CTMC to a piecewise smooth dynamical system.
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