### Abstract

The interplay of random phenomena with discrete-continuous dynamics deserves increased attention in many systems of growing importance. Their verification needs to consider both stochastic behaviour and hybrid dynamics. In the verification of classical hybrid systems, one is often interested in deciding whether unsafe system states can be reached. In the stochastic setting, we ask instead whether the probability of reaching particular states is bounded by a given threshold. In this thesis, we consider stochastic hybrid systems and develop a general abstraction framework for deciding such problems. This gives rise to the first mechanisable technique that can, in practice, formally verify safety properties of systems which feature all the relevant aspects of nondeterminism, general continuous-time dynamics, and probabilistic behaviour. Being based on tools for classical hybrid systems, future improvements in the effectiveness of such tools directly carry over to improvements in the effectiveness of our technique. We extend the method in several directions. Firstly, we discuss how we can handle continuous probability distributions. We then consider systems which we are in partial control of. Next, we consider systems in which probabilities are parametric, to analyse entire system families at once. Afterwards, we consider systems equipped with rewards, modelling costs or bonuses. Finally, we consider all orthogonal combinations of the extensions to the core model.

Original language | English |
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Publication status | Published - 2013 |

Externally published | Yes |