ABSTRACT. Timed automata and hybrid systems are important frameworks for the analysis of continuous-time systems. In this ongoing work, we study a stochastic extension of the latter. There are clear challenges regarding decidability: (i) the reachability problem is already quickly undecidable for non-stochastic hybrid systems; (ii) even in the simpler setting of timed automata, the finite abstraction known as the region graph does not preserve its correctness when lifting it to the stochastic setting. Our goal is to define the class of stochastic o-minimal hybrid systems (SoHSs) and to show that it ensures good properties while being reasonably rich (e.g., it encompasses continuous-time Markov chains). We look for decisiveness of SoHSs (as introduced by Adbulla et al.) and definability in our o-minimal structure. Hopefully, approximation of reachability probabilities could be obtainable in appropriate (and still quite rich) structures.